Trigonometric Identities Question 150
Question: If $ \cos \theta -\sin \theta =\sqrt{2}\sin \theta , $ then $ \cos \theta +\sin \theta $ is equal to
[WB JEE 1988]
Options:
A) $ \sqrt{2}\cos \theta $
B) $ \sqrt{2}\sin \theta $
C) $ 2\cos \theta $
D) $ -\sqrt{2}\cos \theta $
Show Answer
Answer:
Correct Answer: A
Solution:
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 . $
BETA
