First slide

Trigonometric equations

Question

General solution of trigonometric equation $\sqrt{1 - \cos x} = \sin x$

Moderate

A

$n π \pm \frac{π}{2}$
B

$2 n π \pm \frac{π}{2}$
C

$(2 n + 1) \frac{π}{2}$ or $2 n π$
D

no solution

Solution

$\sqrt{1 - \cos x} = \sin x$ , here $\sin x \geq 0$
$\Rightarrow x \in [2 n π, (2 n + 1) π]$
$Also 1 - \cos x = \sin^{2} x$
$\Rightarrow 1 - \cos x = 1 - \cos^{2} x$
$\Rightarrow \cos^{2} x - \cos x = 0$
$\Rightarrow \cos x = 0 o r \cos x = 1$
$\Rightarrow x = n π + \frac{π}{2}$ or $x = 2 n π$

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