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Prove the following (4 sin(θ) cos(θ))(1 − 2 sin2 (θ)) = sin(4θ) cos(2θ) /1 + sin(2θ)...

Prove the following

(4 sin(θ) cos(θ))(1 − 2 sin2 (θ)) = sin(4θ)

cos(2θ) /1 + sin(2θ) = cot(θ) − 1/ cot(θ) + 1

cos(u) /1 + sin(u) + 1 + sin(u) /cos(u) = 2 sec(u)

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