Prove the following trigonometric identities.(i) cot θ-tan θ=2 cos2 θ-1sin θ cos θ(ii) tan θ-cot θ=2 sin2 θ-1sin θ cos θ(iii) sin A-2sin3 A2cos3 A-cos A=tan A

Prove the following trigonometric identities.(i) cot θ-tan θ=2 cos2

1.	Prove the following trigonometric identities.(i) cot θ-tan θ=2 cos2 θ-1sin θ cos θ(ii) tan θ-cot θ=2 sin2 θ-1sin θ cos θ(iii) sin A-2sin3 A2cos3 A-cos A=tan A
Answer» Prove the following trigonometric identities. (i) $\cot θ - \tan θ = \frac{2 \cos^{2} θ - 1}{\sin θ \cos θ}$ (ii) $\tan θ - \cot θ = \frac{2 \sin^{2} θ - 1}{\sin θ \cos θ}$ (iii) $\frac{\sin A - 2 \sin^{3} A}{2 \cos^{3} A - \cos A} = \tan A$