SOLUTION: p tanθ = tan pθ, then find p sin^2 θ; / sin^2 pθ;

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Question 835917: p tanθ = tan pθ, then find p sin^2 θ; / sin^2 pθ;
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
If
(1) p%2Atan%28x%29+=+tan%28px%29
Then what is
(2) p%2Asin%5E2%28x%29%2Fsin%5E2%28px%29
Solve (1) for p to get
(3) p+=+tan%28px%29%2Ftan%28x%29
Now put p of (3) into (2) and get
(4) %28tan%28px%29%2Ftan%28x%29%29%2A%28sin%5E2%28x%29%2Fsin%5E2%28px%29%29 or
(5) %28sin%5E2%28x%29%2Ftan%28x%29%29%2A%28tan%28px%29%2Fsin%5E2%28px%29%29
Now use the identity
(6) tan%28x%29+=+sin%28x%29%2Fcos%28x%29
to get
(7) %28sin%28x%29%2Acos%28x%29%29%2A%281%2F%28cos%28px%29%2Asin%28px%29%29%29
Now use the identity
(8) sin%28x%29%2Acos%28x%29+=+sin%282%2Ax%29%2F2
to get
(8) %28sin%282%2Ax%29%2Fsin%282%2Apx%29%29%29
Answer: p%2Asin%5E2%28x%29%2Fsin%5E2%28px%29+=+sin%282%2Ax%29%2Fsin%282%2Apx%29