If 2 1+ 2 =1 7 and 1- 2 2 =1 10 , (0, 2 ), then ( +2 ) is equal t… - Vidyadip

MCQ

If $\frac{\sqrt{2} \sin \alpha}{\sqrt{1+\cos 2 \alpha}}=\frac{1}{7}$ and $\sqrt{\frac{1-\cos 2 \beta}{2}}=\frac{1}{\sqrt{10}}$ $\alpha, \beta \in\left(0, \frac{\pi}{2}\right),$ then $\tan (\alpha+2 \beta)$ is equal to

✓
$1$
B
$2$
C
$2.5$
D
$3.5$

✓

Answer

Correct option: A.

$1$

a
$\frac{\sqrt{2} \sin \alpha}{\sqrt{2} \cos \alpha}=\frac{1}{7} \Rightarrow \tan \alpha=\frac{1}{7}$

$\sin \beta=\frac{1}{\sqrt{10}} \Rightarrow \tan \beta=\frac{1}{3} \Rightarrow \tan 2 \beta=\frac{3}{4}$

$\tan (\alpha+2 \beta)=\frac{\tan \alpha+\tan 2 \beta}{1-\tan \alpha \tan 2 \beta}=1$

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