Trigonometrical Equations
medium

જો $\sqrt 3 \cos \,\theta + \sin \theta = \sqrt 2 ,$ તો $\theta $ નો વ્યાપક ઉકેલ મેળવો.

A

$n\pi + {( - 1)^n}\frac{\pi }{4}$

B

${( - 1)^n}\frac{\pi }{4} - \frac{\pi }{3}$

C

$n\pi + \frac{\pi }{4} - \frac{\pi }{3}$

D

$n\pi + {( - 1)^n}\frac{\pi }{4} - \frac{\pi }{3}$

Solution

(d) $\frac{{\sqrt 3 }}{2}\cos \theta + \frac{1}{2}\sin \theta = \frac{{\sqrt 2 }}{2}$     { dividing by $\sqrt {{{(\sqrt 3 )}^2} + {1^2}} = 2 $}

$ \Rightarrow $ $\sin \left( {\theta + \frac{\pi }{3}} \right) = \frac{1}{{\sqrt 2 }} = \sin \left( {\frac{\pi }{4}} \right)$

$ \Rightarrow $ $\theta = n\pi + {( – 1)^n}\frac{\pi }{4} – \frac{\pi }{3}$.

Standard 11
Mathematics

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