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  4. If θ + φ = (π/4), then (1+ tan θ)(1+ tan φ) is equal to

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

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Solution:

$(1+\tan \theta) (1+\tan \phi) $
$=(1+\tan \theta)\left[1+\tan \left(\frac{\pi}{4}-\theta\right)\right] $
$=(1+\tan \theta)\left[1+\frac{1-\tan \theta}{1+\tan \theta}\right] $
$=(1+\tan \theta) \cdot \frac{2}{(1+\tan \theta)}=2 $