Question

If $\theta +\varphi =\frac{\pi }{4}$, then $(1+\tan \theta )(1+\tan \varphi )$ is equal to

• A. $1$
• B. $2$
• C. $\frac{5}{2}$
• D. $\frac{1}{3}$

Answer 1

Answer: (B)

$2$

$\theta +\varphi =\frac{\pi }{4}$, then $(1+\tan \theta )(1+\tan \varphi )$

$=(1+\tan \theta )[1+\tan (\frac{\pi }{4}-\theta )]$

$=(1+\tan \theta )[1+\frac{1-\tan \theta }{1+\tan \theta }]$

$=(1+\tan \theta ).\frac{2}{(1+\tan \theta )}=2$