Solve the trigonometric equation?

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April 28th 2009, 07:31 AM
fardeen_gen

Solve the trigonometric equation?

Solve the equation for x:
$\left(\frac{1 - a\sin x}{1 + a\sin x}\right)\sqrt{\frac{1 + 2a\sin x}{1 - 2a\sin x}} = 1,\ a\in\mathbb{R}$
April 28th 2009, 08:15 AM
running-gag

Quote:

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 (Happy)

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