Question

Simplify sine theta over square root of the quantity 1 minus sine squared theta.

Answer 1

$\frac{sin( x)}{ \sqrt{1- (sin(x))^{2} } } = \frac{sin (x)}{ \sqrt{ (cos(x))^{2} } } = \frac{sinx}{cos x} =tan (x)$

Answer 2

Answer with explanation:

In the problem ,theta is replaced by A.

Use the following trigonometric identity to solve the problem

$1.sin^2A+cos^2A=1\\\\2.tan A=\frac{sinA}{cosA}$

The Given function is

$\frac{sin A}{\sqrt{1-sin^2A}}\\\\= \frac{sinA}{\sqrt{cos^2A}}\\\\=\frac{sinA}{cosA}\\\\=tan A$