Trigonometric Identities Question 318
Question: If $ 2\tan A=3\tan B, $ then $ \frac{\sin 2B}{5-\cos 2B} $ is equal to
[AMU 2001]
Options:
A) $ \tan A-\tan B $
B) $ \tan (A-B) $
C) $ \tan (A+B) $
D) $ \tan (A+2B) $
Show Answer
Answer:
Correct Answer: B
Solution:
$ 2\tan \Alpha =3\tan B $
Þ $ \tan A=\frac{3}{2}\tan B=\frac{3}{2}t $ , [Let $ \tan B=t $ ]
Þ $ \sin 2B=\frac{2t}{1+t^{2}},\cos 2B=\frac{1-t^{2}}{1+t^{2}} $ \ $ \frac{( \frac{2t}{1+t^{2}} )}{5-( \frac{1-t^{2}}{1+t^{2}} )} $ $ =\frac{2t}{4+6t^{2}}=\frac{t}{2+3t^{2}}=\tan (A-B) $ .
BETA
