Question

Prove this if ur genius

Answer 1

$\dfrac{\sin \theta -2\sin^3 \theta}{2\cos^3 \theta-\cos \theta}=\tan \theta\\\\\dfrac{\sin \theta(1 -2\sin^2\2 \theta)}{\cos \theta(2\cos^2 \theta-1)}=\tan \theta\\\\\dfrac{1 -2\sin^2\theta}{2\cos^2-1}=1\\\\1-2\sin^2 \theta=2\cos^2 \theta-1\\2\sin^2 \theta+2\cos^2 \theta=2\\\boxed{\sin^2 \theta+\cos^2 \theta=1}$