Trigonometric Identities Question 228
Question: If $ a,\cos 2\theta +b,\sin 2\theta =c $ has a and b as its solution, then the value of $ \tan \alpha +\tan \beta $ is
[Kurukshetra CEE 1998]
Options:
A) $ \frac{c+a}{2b} $
B) $ \frac{2b}{c+a} $
C) $ \frac{c-a}{2b} $
D) $ \frac{b}{c+a} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ a\cos 2\theta +b\sin 2\theta =c $
Þ $ a( \frac{1-{{\tan }^{2}}\theta }{1+{{\tan }^{2}}\theta } )+b\frac{2\tan \theta }{1+{{\tan }^{2}}\theta }=c $
$ \Rightarrow $ $ a-a{{\tan }^{2}}\theta +2b\tan \theta =c+c{{\tan }^{2}}\theta $
$ \Rightarrow $ $ -(a+c){{\tan }^{2}}\theta +2b,\tan \theta +(a-c)=0 $
$ \therefore \tan \alpha +\tan \beta =-\frac{2b}{-(c+a)}=\frac{2b}{c+a} $ .
BETA
