Trigonometric Identities Question 63
Question: If $ A+B+C=\pi $ and $ \cos A=\cos B\cos C, $ then $ \tan B\tan C $ is equal to
[AMU 2001]
Options:
A) $ \frac{1}{2} $
B) 2
C) 1
D) $ -\frac{1}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \cos [\pi -(B+C)]=\cos B\cos C $
Þ $ -\cos (B+C)=\cos B\cos C $
Þ $ -[\cos B\cos C-\sin B\sin C]=\cos B\cos C $
Þ $ \sin B\sin C=2\cos B\cos C $
Þ $ \tan B\tan C=2 $ .
BETA
