SOLUTION: prove the following identity cos (x)/sec(x)-cot (x)/tan (x)=cos^2 (x)-cot^2(x)

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Question 1091264: prove the following identity cos (x)/sec(x)-cot (x)/tan (x)=cos^2 (x)-cot^2(x)
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!

sec(x) is the reciprocal of cos(x), so
cos%28x%29%2Fsec%28x%29+=+cos%28x%29%2F%281%2Fcos%28x%29%29+=+cos%5E2%28x%29

Similarly, tan(x) is the reciprocal of cot(x), so
cot%28x%29%2Ftan%28x%29+=+cot%28x%29%2F%281%2Ftan%28x%29%29+=+cot%5E2%28x%29

And so the left hand side of the identity is
cos%5E2%28x%29+-+cot%5E2%28x%29
which is equal to the right hand side, and we are done.