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Simplify: cos2θ1sin2θ...

Simplify: cos2θ1sin2θ

A.

tanθ

B.

cosθ

C.

tanθ

D.

cosθ

Correct answer is A

cos2θ1sin2θ

cos(x+y)=cosxcosysinxsinycos2θ=cos2θsin2θ

cos2θ=1sin2θcos2θ=12sin2θ

sin2θ=2sinθcosθ

= \frac{-2 \sin^{2} \theta}{2\sin \theta \cos \theta} = \frac{- \sin \theta}{\cos \theta}

= -\tan \theta