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Trigonometrical Equations
easy
यदि $\sin \theta + \cos \theta = \sqrt 2 \cos \alpha $, तो $\theta $ का व्यापक मान है
A
$2n\pi - \frac{\pi }{4} \pm \,\,\alpha $
B
$2n\pi + \frac{\pi }{4} \pm \alpha $
C
$n\pi - \frac{\pi }{4} \pm \alpha $
D
$n\pi + \frac{\pi }{4} \pm \alpha $
Solution
(b) $\sin \theta + \cos \theta = \sqrt 2 \cos \alpha$
$\Rightarrow \cos \left( {\theta – \frac{\pi }{4}} \right) = \cos \alpha $
$ \Rightarrow $ $\theta – \frac{\pi }{4} = 2n\pi \pm \alpha $
$\Rightarrow \theta = 2n\pi + \frac{\pi }{4} \pm \alpha $.
Standard 11
Mathematics
