Verify the identity
Here is another way to verify by working on both side together,
cot^2x - cos^2x = cot^2x * cos^2x, where cot^2x = (cos^2x)/(sin^2x)
Substitute cot^2x and multiply the second term with (sin^2x)/(sin^2x) for common denominator
(cos^2x)/(sin^2x) -( cos^2x)(sin^2x)/(sin^2x) = (cos^2x)/(sin^2x) * cos^2x
Multiply by sin^2x on both sides to eliminate denominator and factor, then
cos^2x(1 - sin^2x) = cos^2x * cos^2x
Devide by cos^2x on both sides
1- sin^2x = cos^2x, where 1 - sin^2x = cos^2x
Then, cos^2x = cos^2x, both sides same.
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