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reduction formula for (sinx)^m (cosx)^n with limits 0 to pi/2

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reduction formula for (sinx)^m (cosx)^n with limits 0 to pi/2 in the numerator start off with (m-1) , (n-1) subtract 2 successively till 2 or 1 is reached in the denominator start off with (m+n) , subtract 2 successively till 2 or 1 is reached Also put a pi/2 in the numerator if m and n are both even ----------------------------------------------------------- please leave your comments below ------------------------------------------------------------ index of math problems disclaimer: There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work
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cos[(3pi/4)+x] - cos[(3pi/4)-x] = (-sqrt(2))sinx

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cos[(3pi/4)+x] - cos[(3pi/4)-x] = (-sqrt(2))sinx ncert 11th trigonometry, exercise 3.3 11. prove that cos[(3pi/4)+x] - cos[(3pi/4)-x] = (-sqrt(2))sinx using trigonometry formula trigonometry identities cosx + cosy =2cos[(x+y)/2] cos[(x-y)/2] LHS = cos[(3pi/4)+x] - cos[(3pi/4)-x] =2cos[2(3pi/4)/2] cos[2x/2] =2cos[(3pi/4)] cosx =2{-1 /(-sqrt(2)) } cosx   [cosx is negative in second quadrant] = (-sqrt(2))sinx =RHS 10. prove that sin[(n+1)x]sin[(n+2)x] +cos[(n+1)x]cos[(n+2)x] =cosx using trigonometry formula trigonometry identities cosAcosB +sinAsinB = cos(A-B) A =(n+2)x B=(n+1)x LHS =  sin[(n+1)x]sin[(n+2)x] +cos[(n+1)x]cos[(n+2)x] =cos[A-B] FORM =cos[(n+2)x - (n+1)x ] =cosx =RHS 6. prove that cos[(pi/4)-x]cos[(pi/4)-y]- sin[(pi/4)-x]sin[(pi/4)-y] = sin(x+y) using trigonometry formula trigonometry identities cosAcosB - sinAsinB = cos(A+B) A= [(pi/4)-x] B= [(pi/4)-y] LHS =  cos[(pi/4)-x]cos[(pi/4)-y]- s...
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driving test in trivandrum, kerala

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Before taking the driving test you have to get a learner's license.For that you had to to take an objective test on the computer in the RT office. The questions that are asked correspond to important trafic signs, traffic rules etc. Books are available that contain model questions (usually in malayalam). But I was able to find an online version of the model questions in english. After passing the test you are given a date after several weeks to appear for the driving test which consisted of taking a H test (driving the car in a particular pattern between iron stakes arranged in the shape of an H ; you go forward along one of the vertical lines of the H from bottom to top , then reverse to the middle , go in reverse along the centre horizontal line of the H , and then to the opposite bottom of the other vertical line of the H in reverse , then forward to the top of that vertical line , then reverse to the middle of the vertical line, then in reverse along the central horizontal...
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