Trigonometric Identities Question 323
Question: If $ \sin 2\theta +\sin 2\varphi =1/2 $ and $ \cos 2\theta +\cos 2\varphi =3/2 $ , then $ {{\cos }^{2}}(\theta -\varphi )= $
[MP PET 2000; Pb. CET 2000]
Options:
A) $\frac{3}{8}$
B) $ A+B+C=\pi , $
C) $\frac{3}{4}$
D) $ 5/4 $
Show Answer
Answer:
Correct Answer: B
Solution:
Given $ \sin 2,\theta +\sin 2\varphi =1/2 $ ?..(i) and $ \cos 2,\theta +\cos 2,\varphi =3/2 $ ?..(ii) Square and adding,
$ \therefore ,({{\sin }^{2}}2\theta +{{\cos }^{2}}2\theta )+({{\sin }^{2}}2\varphi +{{\cos }^{2}}2\varphi ) $ $ +2,[\sin 2,\theta ,\sin 2,\varphi +\cos 2,\theta ,\cos 2,\varphi ]=1/4+9/4 $
Þ $ \cos 2\theta \cos 2\varphi +\sin 2\theta \sin 2\varphi =1 $
Þ $ \cos (2\theta -2\varphi )=1/4 $
Þ $ {{\cos }^{2}}(\theta -\varphi )=5/8 $ .
BETA
