but the main intention of the series is that you have to get the answer in 60 seconds okay so you think market for example we are then questioned in fact these questions come in 2021. see there are two negative values to positive one that means the examiner the person who's sitting the paper is expecting you to get rid of negative values to get rid of positive values you have to eliminate and also i also made i think i already made a video like how to solve uh any k-state equation 60 seconds on video monitoring and i've discussed like various methods like elimination method reverse [Music] like ten seconds ago in the camera if you just know the property so if you i know uh function we assigned it a function and even another zero to two pi integrate i love integration i just love calculus very much okay if you integrate sine theta from zero to two pi definitely the value of one zero came together whatever the positive values you have the same negative values this is that's the reason why adding the you know this one you know integrating the the sine function from zero to point obviously zero just adding all the values are so we learn to answer 0 that's the only thing if you just know this property it's done it is if we just integrate the same terms from 0 to but it will be very zero it is first question second inland himself if you see some properties limited so it's suppose if sine theta 1 plus sine theta delta if you have assigned it down to sine 0 that must be equal if it is 0 this can be 0 theta 1 plus theta 2 must be equal to if it is 360 degrees on the property in that you see nothing but every time you can't remember properties that's the reason why i say there's a conceptual understanding is very important so theta one plus theta is zero data out there when you see sine theta one plus sine is zero when determined plus theta is pleasing degrees in particular it's more easy if you just know astc rule that's more easy single practice is the very very important trigonometry you should know this okay so very simply for example you can unsign one degree or enough sign three fifteen thousand three final i can write this also as if i want i can write this as sine for example uh 360 that is 2 pi sine 2 pi minus 1 degree in the parabola this sine 3 359 sine 360 minus 1 variable so what is sine three pi minus one degree it's negative coordinates it will come in fourth quadrant and then zero to two pi for example zero to two pi one circle as well two pi minus other side fourth quadrant the fourth quadrant notice for example you can clearly see that it's cos sine is negative actually therefore i'm getting again now to the minus sign one degree above that under you know so plus sine one degree minus one degree cancel out with that at r plus sine one degree minus sign one day before three free know [Music] 360 degrees then sign it down plus center zero degree knew every time you can't remember if the property is good there are thousands of properties like this i can't get so many properties instead of that if you just know a stc rule it's more easy right you can just say sine 359 is like sine two pi minus one degrees minus sine other three six into two by seven twenty and then four pi four pi fourteen fourteen eight pi then we have either the question one you should be able to write in terms of smaller angles no really non vector tan eight pi and the tan first quarter was first positive is the diamond forty stand eight pi plus forty finds a forty five degree neighbor of the nine forty five and forty five value step by ten forty five value and forty five monday one actually two eight so this value is one so is so my answer is what i need to get one plus something what is this something cos thousand two hundred think new yeah you go over to what they cost thousand two hundred convert money you should know how to eliminate the option that is very important one plus something in it so the total answer of this value cos thousand two hundred plus cos thousand four eighty five that should be in between zero and two that means there's no negative value negative value chances are negative um [Music] a thousand eighty one okay now and then three point two minus six five so six pi plus one twenty in the body one there's six pi plus theta but obviously six five plus two upon the cost is just thousand four eighty five so answer positive will make one plus something positive then which helps you know to get the value of two i will teach this method and get more methodologies three methods to teach marketing don't worry and also methods also important please subscribe [Music] so 45 degree 45 degree arc is about 32 actually so 10 45 one got 45 months one plus one is two if this is satisfying so directly forty five forty five you know forty five ninety forty five plus forty five star power one plus two will just answer want these methods for you not even under that substitution it's always remember that's why i told you then they have done a video right i've made a video on how to solve under 60 seconds of doing video and i told you substitution method and reverse solving method elimination method you should know all this this is like a substitution whether you're substituting something and then getting that okay first actually okay so methods danny plus answer tomorrow i'll just show the steps okay and already explain more than you think about that no problem so got four a plus two tan square into quadsquad two into tan square into square a plus chord and we know material code is really you know by normal expansion it's more easy actually okay so whenever we have it you know like we have something like tan a plus you know suppose you imagine that we have like x plus y you need to find something like you know x plus y x to the power of six and y to the power of six and the binomials are expo four alvaro formula y four and binomial expression binomial expansion yeah of the book called the initial method actually explore four y four four alpha you let us try binomial expansion because i can expand if you just expand this four times then that is fine mine expansion is done so i will get the single equation if i had so the easily errors at the moment you know tan and plus i caught the whole square multimeter square model your single equation foreign so then i'll do little faster okay so let's see that the coefficient is going to be the one five here one four six four one right now even i told you with trigonometry when i told the same thing in the normal distribution in np the technology is almost please go and check if you don't remember normal distribution even kc design 2022 uh how to get a how to get a good rank in case it is the same thing i've told you like on graph architecture one four six four one okay may look killed above actually coefficients are they do how to calculate distance again you have to use n c one and c two and anything like that but you don't have to worry about that there's something called pascal's triangle okay i don't use markup so i'm just doing a little faster okay uh tanya please caught it to the power of four and kill them uh two to two to four more to the four photos if you just get you know uh if there are six plus four into 10 plus quarter common down 10 plus quarter of the four plus two eight and plus you have to find this value so 16 uh four twos are 12 12 6 you know sorry eight eight plus six eight plus six fourteen fourteen minus six is sixteen is answer is uh fourteen you know fourteens two answer is i'm getting answers to here also i think you know what i understood let me explain that if you don't wanna learn this step please move on so next question uh skip mark but if someone want to learn please learn this this is very helpful okay okay what i meant to say is scotty foreign m is equal to x into 4 into 2 8 plus 6 this will be x is equal to for 16 minus ah 8 plus 6 just about the 14 alpha so 2 1 and then [Music] a given question can be solved in many many methods and and that is a beauty of competitive exam let's go for the next question now so mother as in the similar type of questions i think we're discussing till now if you have tan theta one time you have to multiply whatever and so on you know this is one if theta one plus theta two is equal to ninety degrees and 45 degree value you know and 45 degree value one is option nine seven and one here it will cancel out that time one no time cancel out the time two mother tan 88 cancel the tan three mother ten eighty seven cancel out the stan 87 can written as so my favorite is trigonometry okay remember this very beautiful subject okay cos square 45 value of stuff cos square 45 cos square root of 45 in the cos quantity one by row two one by two square one by two and one by two one the point five is let me say something value is that but it's a very damn sure i'm very damn sure since 15 is positive degrees it's a positive value if you want to guess the value also x is much much greater than r therefore x can be negative r can be greater than the lte if you remember a lot of derivations okay so 0.2 square more like the foreign point eight five two point seven divided by two almost sorry two point seven divided by two and then one point two three five number of that one point three five eight by root two root two only one point four so one point three five by one point four so then we calculated one point one by two is the point data answer should be less than point five so we have to do it i don't know right root three by four is the per root three by two origin with two point eight and the root three by four minus point eight to half a point four somewhere our answer is matching so point five minus answer we have to know that again approximately point four four point four three number eight point four you know exactly option b north average point four but i there but you need to confirm once with this answer root three is divided by two that is point three five point three percent divided by one point uh root two is one point four one so whatever so this value is too small point three value one point four is less you know basic requirement is you have to be able to guess the values to see some videos you know like uh without studying it uh without studying it party how to trick without answering this is all concept concept is important okay next question okay what is visualized [Music] this [Applause] [Music] two cos square theta minus one of the beautiful formula which converts square terms which converts square term into a costume square controller formulas two of pi by eight and then pi by four divided by and the two cos into cos either another point two cos squared over the new denominatory one shift 21 plus cost and one plus nine game you know the cause to cos 2 determine cos 2 times of pi by pi by 8 and then pi by 4 cos pi by 4 e either substitute multiple actually sine waveform i know one by root o cos peripheral one by root two only one by one by root two divided by 1 plus 1 by root 2 and you answer 1 by 4 so you're gonna so you shift more than mk 1 by root 2 divided by root 2 plus 1 divided by root 2 to cancel out there one divided by root 2 plus 1 at the moment it's very clear okay next question let's go to this question now and it happens quarter is equal to order plus 10 is so with the if you want to put this you know a solution we want to put the solution to the answer what happens basically n value is there here the n is the problem actually so take n as zero and zero because the only integer alpha if you know any plus cortex they ask me to find general solution questions on uh easy questions actually i mean if you study it's very easy okay if you understand okay so substitute for plus minus 1 to the power of n into pi by 2 i think okay so i told you how to solve 6 seconds we just solved it but actual method of solving knowledge new information okay general solution sine x equals sine way cos is equal to cos x cos x is equal to cosine is equal to y the general solution formulas so caught uh this is i can write like sine theta yeah theta that must be equal to one so cross multiply body you'll get like cos square theta so cos square plus uh sine square theta the element sign in the cosine actually when you have sine theta and cos theta uh to your salva a one year earlier okay fine no issues uh oh you do either sorry see solving actually solving uh quickly solving is more easy than doing all these steps okay significant to sine pi by down thousand i know so you know the two t alpha so sine x is equal to sine y one value matra uh sine y is equal to n something like if you are like this then it's y is equal to the formula is uh n pi uh plus minus one to the power of n into pi by two on the vertical general solution of n pi plus minus one to the power pi by delta so two to the ordering pi weight over there uh two theta must be equal to now so two theta must be equal to uh n pi uh plus minus 1 to the power of n into e place here n is alpha sorry x on the vertical x whatever is that that will come okay x okay the expression of the pi by 2 and is pi by 2 minus 1 to the power of n pi by to the half oh by by from the whole terminal two terminal half on the multiply by um half of the multiplied by okay now okay so i've got an answer on the b and this is this is the beauty of mathematics 1 plus 10 square so 1 plus 10 squared i just started i'm just doing it i don't think so i don't know whether we can do it this way let's try that okay i just took it now so no no no no no equation convert mode right just minus 2 times this one is zero okay um x square minus two x plus one that is x minus uh one the whole square that means this is tan theta minus one the whole square equal to zero and then tan theta must be equal to one that means here we get tan theta must be equal to tan pi by 4 if tan x is equal to tan y then x is equal to n pi plus or minus whatever that value you get that's pi by 4. so it looks like both of these are known both are not different actually if you substitute the values you get same answer let's imagine now if i put n is 0 0 0 0 0 that's a beauty okay even though we sort of different method anyway optionally likely they don't have an option that n pi plus pi minus probably one word this was the answer and and then generally you can solve in many ways students trying in different different methods either anyway let's go for next question now the oneplus 6 okay this isn't see whenever you see something like in five terms okay just go with ap gp series we have a beautiful chapter method is called sequence and very very quickly just know it's nothing nothing but a gp it's a gp terminal it's a gp right so gp android uh you know the common ratio what is sine theta by one so sum of infinite terms of a gp terms is if you know the formula is one minus one by r then it's done the ratio is tinted by one sine square divided by sign it again so you get the what is [Music] minus three pi by four is there but it's nothing but five minus pi by four again it will be in terms of pi by four only so uh root three actually so last you get two scientific degrees yesterday seconds the actual method of solving but here is null already is x harmonic more than one method one methodology a little more method actually but you have to use your brain tell you is more like okay not a board exams where fixed questions will come everything will come to different different methods okay 60 questions in mathematics 45 questions 45 to 50 questions can be answered in 60 seconds and then bitcoin but there is no short trade for everything but equations the concept you know there are something like some texts will be there is for example some substitution is called zero you may say it's some kind of trick actually but it's not always it's more about concept than the short tricks and everything okay so i hope you understood this uh video and i hope you love this session and thank you so much for watching guys have a nice day see you next video bye bye take care