Question

How do I verify the following trigonometric identity? Cot^2x-cos^2x/csc^2x-1=cos^2x

Answer 1

Please see below.

Explanation:

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`(cot^2x-cos^2x)/(csc^2x-1)= (cos^2x/sin^2x-cos^2x)/(1/sin^2x-1)=((cos^2x-sin^2xcos^2x)/sin^2x)/((1-sin^2x)/sin^2x)=(cos^2x-sin^2xcos^2x)/(1-sin^2x)=(cos^2x(1-sin^2x))/(1-sin^2x)=cos^2x`