If (1 + tan θ )(1 + tan phi ) = 2 , then θ + phi = .... ^o

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Trigonometrical Equations

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

A

${30}$

B

${45}$

C

${60}$

D

${75}$

Solution

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

Standard 11

Mathematics

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