JEE PYQ: Trigonometric Ratios And Identities Question 5
Question 5 - 2020 (08 Jan Shift 2)
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 ______
Type: Numerical
Show Answer
Answer: 1
Solution
$\tan\alpha = \frac{1}{7}$, $\sin\beta = \frac{1}{\sqrt{10}} \Rightarrow \tan\beta = \frac{1}{3}$. $\tan 2\beta = \frac{3}{4}$. $\tan(\alpha + 2\beta) = \frac{\frac{1}{7}+\frac{3}{4}}{1-\frac{3}{28}} = 1$.
BETA
