Question

Tan^2xsin^2x=tan^2x-sin^2x
Prove identity

Answer 1

See below for proof

Explanation:

`\tan^2x\sin^2x\\\\(\sec^2x-1)(\sin^2x)\\\\((1)/(\cos^2x)-(\sin^2x)/(\sin^2x))(\sin^2x)\\\\((\sin^2x-\sin^2x\cos^2x)/(\sin^2x\cos^2x))(\sin^2x)\\\\(\sin^2x-\sin^2x\cos^2x)/(\cos^2x)\\\\(\sin^2x)/(\cos^2x)-\sin^2x\\\\\tan^2x-\sin^2x`

Hence, the identity is proven