Proving the identity $\tan (A)-\sin^2(A)\tan(A) = \cos(A)\sin(A)$

Question

I came across an interesting question while studying for AS Levels.

Prove the following identity: $$\tan (A)-\sin^2(A)\tan(A) = \cos(A)\sin(A)$$

Hints and suggestions on how to solve this?

Answer 1

Note that

$$\tan A-\sin^2 A\tan A=\tan A(1-\sin^2 A)=\tan A\cos^2 A=\frac{\sin A}{\cos A}\cos^2 A=\sin A\cos A$$