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

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) (Show Source): You can put this solution on YOUR website!

sec(x) is the reciprocal of cos(x), so

Similarly, tan(x) is the reciprocal of cot(x), so

And so the left hand side of the identity is

which is equal to the right hand side, and we are done.

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