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Trigonometrical Equations
easy
સમીકરણ $\cos 2\theta = \sin \alpha ,$ નું સમાધાન કરે તેવા $\theta $ નો વ્યાપક ઉકેલ મેળવો.
A
$2\theta = \frac{\pi }{2} - \alpha $
B
$\theta = 2n\pi \pm \left( {\frac{\pi }{2} - \alpha } \right)$
C
$\theta = \frac{{n\pi + {{( - 1)}^n}\alpha }}{2}$
D
$\theta = n\pi \pm \left( {\frac{\pi }{4} - \frac{\alpha }{2}} \right)$
Solution
(d) $\cos 2\theta = \cos \left( {\frac{\pi }{2} – \alpha } \right)$
$\Rightarrow 2\theta = 2n\pi \pm \left( {\frac{\pi }{2} – \alpha } \right)$
$ \Rightarrow $ $\theta = n\pi \pm \left( {\frac{\pi }{4} – \frac{\alpha }{2}} \right)$.
Standard 11
Mathematics
