If (1 + )(1 + ) = 2, then + = ....^o - Vidyadip

MCQ

If $(1 + \tan \theta )(1 + \tan \phi ) = 2$, then $\theta + \phi =$ ....$^o$

A
${30}$
✓
${45}$
C
${60}$
D
${75}$

✓

Answer

Correct option: B.

${45}$

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

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

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

$ \Rightarrow $ $\theta + \phi = \frac{\pi }{4} = 45^\circ$.

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