SOLUTION: if a sin^3 theta+b cos^3 theta=sin theta cos theta and a sin theta-b cos theta =0 then prove that a^2+b^2=1

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Question 782104: if a sin^3 theta+b cos^3 theta=sin theta cos theta and a sin theta-b cos theta =0 then prove that a^2+b^2=1
Answer by mananth(16946) About Me  (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