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3.Trigonometrical Ratios, Functions and Identities
medium
If $\cos \theta - \sin \theta = \sqrt 2 \sin \theta ,$ then $\cos \theta + \sin \theta $ is equal to
A
$\sqrt 2 \cos \theta $
B
$\sqrt 2 \sin \theta $
C
$2\cos \theta $
D
$ - \sqrt 2 \cos \theta $
Solution
(a) We have $\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
