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# Solve (cos² x - sin² x) / (cos² x + sin x cos x) = 1 - tan x?

using identities

tanx = sinx/cosx andd

cos^2 x + sin^2 x = 1

### 1 Answer

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- mohanrao dLv 79 years agoFavorite Answer
The given problem is to prove the identity, not to solve

(cos² x - sin² x) / (cos² x + sin x cos x)

= ( cos x + sin x)(cos x - sin x) / cos x( cos x + sin x)

= (cos x - sin x) / cos x

= ( cos x / cos x ) - ( sin x / cos x )

= 1 - tan x

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