LHS:

For numerator use formula

a^2 - b^2 = (a-b)(a+b)

So

cos^2(x) - sin^2 (x) = (cos(x) - sin(x))(cos(x) + sin(x))

Denominator

cos^2(x) +cos(x)sin(x) = cos(x)(cos(x) +sin(x))

Divide numerator by denominator

The things in bold get cancelled

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One more thing try to avoid writing like thissssssss

Adarsh