Question

Simplify sin theta/sqrt 1-sin^2 theta

Answer 1

`\frac{\sin(\theta)}{\sqrt{1-\sin(\theta)^(2)}}=(\sin(\theta))/(\cos(\theta))\\\\=\tan(\theta)`

Answer 2

`\text{Use:}\\\sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\\\\\tan x=(\sin x)/(\cos x)`


`(\sin\Theta)/(√(1-\sin^2\Theta))=(\sin\Theta)/(√(\cos^2\Theta))=(\sin\Theta)/(\cos\Theta)=\tan\Theta`