Trigonometric Identities Question 26
Question: If $ \cos (A-B)=\frac{3}{5} $ and $ \tan A\tan B=2, $ then
[MP PET 1997]
Options:
A) $ \cos A\cos B=\frac{1}{5} $
B) $ \sin A\sin B=-\frac{2}{5} $
C) $ \cos A\cos B=-\frac{1}{5} $
D) $ \sin A\sin B=-\frac{1}{5} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \cos ,(A-B)=\frac{3}{5} $ \ $ 5\cos A\cos B+5\sin A\sin B=3 $ ?..(i) From 2nd relation, $ \sin A\sin B=2\cos A\cos B $ …..(ii)
$ \therefore $ $ \cos A\cos B=\frac{1}{5} $ and $ 5,( \frac{1}{2}+1 ),\sin A\sin B=3 $ .
BETA
