The general value obtained from the equation 2 = is - Vidyadip

MCQ

The general value $\theta$ obtained from the equation $\cos 2 \theta=\sin \alpha$ is

A
$2 \theta=\frac{\pi}{2}-\alpha$
B
$\theta=2 n \pi \pm\left(\frac{\pi}{2}-\alpha\right)$
C
$\theta=\frac{ n \pi+(-1)^{ n } \alpha}{2}$
✓
$\theta=n \pi \pm\left(\frac{\pi}{4}-\frac{\alpha}{2}\right)$

✓

Answer

Correct option: D.

$\theta=n \pi \pm\left(\frac{\pi}{4}-\frac{\alpha}{2}\right)$

(D) $\cos 2 \theta=\sin \alpha$
$\Rightarrow \cos 2 \theta=\cos \left(\frac{\pi}{2}-\alpha\right)$
$\begin{array}{l}\Rightarrow 2 \theta=2 n \pi \pm\left(\frac{\pi}{2}-\alpha\right) \\ \Rightarrow \theta= n \pi \pm\left(\frac{\pi}{4}-\frac{\alpha}{2}\right)\end{array}$

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