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

Correct answer: (B) 2. Hints: (1+tan θ) (1+((1-tan θ))/(1+tan θ) ) =(1+tan θ) 2/(1+tan θ)=2

Q56 / 160 · WBJEE 2011 · Mathematics

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

A
1
Correct answer
B
2
C
\(5 / 2\)
D
\(1 / 3\)

Solution

\(\begin{aligned} & \text { Hints: }(1+\tan \theta)\left(1+\frac{(1-\tan \theta)}{1+\tan \theta}\right) \\ & =(1+\tan \theta) \frac{2}{1+\tan \theta}=2 \end{aligned}\)

Hence, the correct answer is option: 'B'.

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

Solution

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