Trigonometric Identities Question 146
Question: If $ \frac{\cos A}{\sin B\sin C}+\frac{\cos B}{\sin C\sin A}+\frac{\cos C}{\sin A\sin B}= $ then $ 32\sin ( \frac{A}{2} )\sin ( \frac{5A}{2} )= $
[DCE 1996]
Options:
A) 7
B) 8
C) 11
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ 32\sin \frac{A}{2}\sin \frac{5A}{2}=16(\cos 2A-\cos 3A) $ $ =16(2{{\cos }^{2}}A-1-4{{\cos }^{3}}A+3\cos A) $ $ =16( 2\times \frac{9}{16}-1-4\times \frac{27}{64}+3\times \frac{3}{4} )=11 $ .
BETA
