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

MCQ

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

A
$2\theta = \frac{\pi }{2} - \alpha $
B
$\theta = 2n\pi \pm \left( {\frac{\pi }{2} - \alpha } \right)$
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
(d) $\cos 2\theta = \cos \left( {\frac{\pi }{2} - \alpha } \right)$

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

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

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