3.Trigonometrical Ratios, Functions and Identities
medium

यदि $\cos \theta - \sin \theta = \sqrt 2 \sin \theta ,$ तो $\cos \theta + \sin \theta $ बराबर होगा

A

$\sqrt 2 \cos \theta $

B

$\sqrt 2 \sin \theta $

C

$2\cos \theta $

D

$ - \sqrt 2 \cos \theta $

Solution

(a) चूँकि $\cos \theta  – \sin \theta  = \sqrt 2 \,\sin \theta $

$ \Rightarrow \,\cos \theta  = (\sqrt 2  + 1)\,\sin \theta \, $

$\Rightarrow \,(\sqrt 2  – 1)\cos \theta  = \sin \theta $

$ \Rightarrow \,\sqrt 2 \,\cos \theta  – \cos \theta  = \sin \theta  $

$\Rightarrow \,\sin \theta  + \cos \theta  = \sqrt 2 \,\cos \theta .$

Standard 11
Mathematics

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