JEE PYQ: Trigonometric Ratios And Identities Question 8
Question 8 - 2019 (08 Apr Shift 1)
If $\cos(\alpha + \beta) = \frac{3}{5}$, $\sin(\alpha - \beta) = \frac{5}{13}$ and $0 < \alpha, \beta < \frac{\pi}{4}$, then $\tan(2\alpha)$ is equal to:
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(1) $\frac{63}{52}$
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(2) $\frac{63}{16}$
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(3) $\frac{21}{16}$
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(4) $\frac{33}{52}$
Show Answer
Answer: (2) $\frac{63}{16}$
Solution
$\tan(\alpha+\beta) = \frac{4}{3}$, $\tan(\alpha-\beta) = \frac{5}{12}$. $\tan 2\alpha = \frac{\frac{4}{3}+\frac{5}{12}}{1-\frac{4}{3}\cdot\frac{5}{12}} = \frac{63}{16}$.
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