Question

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

• A. 1
• B. 2
• C. 44683
• D. 44564

Answer 1

Answer: (B)

2

Answer 2

$\frac{\tan\theta+\tan\phi}{1-\tan\theta\tan\phi}=1$

$\tan\theta+\tan\phi=1-tan\phi\tan\phi$

$\tan\phi+\tan\phi+\tan\theta.\tan\phi=1$

$(1+\tan\theta)(1+\tan\phi)=2$