Question

Simplify the expression:
sin^4x cosx/ cos^4x sinx

Answer 1

`tan^3x`

Explanation:

We want to simplify:

`(\sin^4x\cos x)/(\cos^4x\sin x)`

This is the same as:

`(\sin^3x \sin x\cos x)/(\cos^3x \cos x\sin x)`

Cancel out the common factors to get;

`(\sin^3x)/(\cos^3x)`

This is the same as

`((\sin x)/(\cos x) )^3=tan^3x`