SOLUTION: Verify the identity. (cot^2 x) / (cosec x + 1) = (1 - sin x) / sin x

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Question 1106777: Verify the identity.
(cot^2 x) / (cosec x + 1) = (1 - sin x) / sin x

Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


%28cot%28x%29%29%5E2+%2F+%28csc%28x%29+%2B+1%29+=+%281+-+sin+x%29+%2F+sin+x

Work on the left hand side to make it look like the right hand side.

%28%28cos%28x%29%29%5E2%2F%28sin%28x%29%29%5E2%29+%2F+%28%281%2Fsin%28x%29%29%2B1%29 Change everything to sin(x) and cos(x):

get common denominator in the denominator

divide fractions: "flip and multiply"

%28cos%28x%29%29%5E2%2F%28%28sin%28x%29%29%2A%281%2Bsinx%29%29 simplify

%28%281-sin%28x%29%29%5E2%29%2F%28%28sin%28x%29%29%2A%281%2Bsinx%29%29 use Pythgorean identity to get everything in terms of sin(x)

%28%281-sin%28x%29%29%281%2Bsinx%29%29%2F%28%28sin%28x%29%29%2A%281%2Bsinx%29%29 factor

%281-sin%28x%29%29%2Fsin%28x%29 cancel common factor

DONE! The left hand side is now the same as the right hand side.