# Math Help - Solve the trigonometric equation?

1. ## Solve the trigonometric equation?

Solve the equation for x:
$\left(\frac{1 - a\sin x}{1 + a\sin x}\right)\sqrt{\frac{1 + 2a\sin x}{1 - 2a\sin x}} = 1,\ a\in\mathbb{R}$

2. Originally Posted by fardeen_gen
Solve the equation for x:
$\left(\frac{1 - a\sin x}{1 + a\sin x}\right)\sqrt{\frac{1 + 2a\sin x}{1 - 2a\sin x}} = 1,\ a\in\mathbb{R}$
Hi

$\frac{1 + 2a\sin x}{1 - 2a\sin x} = \frac{(1 + a\sin x)^2}{(1 - a\sin x)^2},\ a\in\mathbb{R}$

$(1 + 2a\sin x)(1 - a\sin x)^2 = (1 + a\sin x)^2(1 - 2a\sin x),\ a\in\mathbb{R}$

Expand and simplify