Trigonometric Equations Question 85
Question: If $ (1+\tan \theta )(1+\tan \varphi )=2 $ , then $ \theta +\varphi $ =
[Karnataka CET 1993]
Options:
A) $ 30^{o} $
B) $ 45^{o} $
C) $ 60^{o} $
D) $ 75^{o} $
Show Answer
Answer:
Correct Answer: B
Solution:
- $ (1+\tan \theta )(1+\tan \varphi )=2\Rightarrow \frac{\tan \theta +\tan \varphi }{1-\tan \theta \tan \varphi }=1 $
$ \Rightarrow $ $ \tan (\theta +\varphi )=1 $
$ \Rightarrow $ $ \theta +\varphi =\frac{\pi }{4} $ = 45o.
BETA
