Trigonometric-Equations Question 396

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.