Question

if a sin cube theta + b cos cube theta is equal to sin theta cos theta and a sin theta minus B cos theta is equal to zero then prove that a square + b square is equal to 1​

Answer 1

Answer by mananth(15197) (Show Source): You can put this solution on YOUR website!

a sin^3 theta+b cos^3 theta=sin theta cos theta

a sin theta-b cos theta =0

asin%28+theta%29+=+bcos+%28theta%29

a=+bcos%28theta%29%2Fsin%28theta%29

substitute a in equation a sin^3 theta+b cos^3 theta=sin theta cos theta

bcos%28theta%29%2Asin%5E2%28theta%29%2Bbcos%5E3%28theta%29=sin%28theta%29cos%28theta%29

bcos%28theta%29%28sin%5E2%28theta%29%2Bcos%5E2%28theta%29%29=sin%28theta%29cos%28theta%29

bcos%28theta%29=sin%28theta%29cos%28theta%29

b=sin%28theta%29

Now a=+bcos%28theta%29%2Fsin%28theta%29

substitute b

a= sin(theta).cos(theta)/sin(theta)}}}

so a=+cos%28theta%29

Therefore a%5E2%2Bb%5E2=+sin%5E2%28theta%29%2Bcos%5E2%28theta%29

a%5E2%2Bb%5E2=1