could someone show the steps to verifying this identity, and what was used to solve it?
(cos x − sec x)2 = tan2 x − sin2 x
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just expand the LHS we get LHS = cos^2 - 2 cos x * sec x + sec ^2 x = 1-sin^2x -2 + 1 + tan^2 x and you have the RHS
alternatively you could start with RHS = tan^2x - sin^2x = ( sec^2x - 1 ) - ( 1 - cos^2x) = sec^2x - 2 + cos^2x = sec^2x - 2 secx * cosx+ cos^2x = ( cosx - se x )^2 = LHS
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