[JEE Main 2010] if cos alpha beta 45 sin alpha beta 5 13 with 0 alpha beta
If $\cos(\alpha+\beta)=\frac45$, $\sin(\alpha-\beta)=\frac5{13}$ with $0\le\alpha,\beta\le\frac\pi4$, then $\tan2\alpha$ equals
(a) $\frac{56}{33}$
(b) $\frac{19}{12}$
(c) $\frac{20}7$
(d) $\frac{25}{16}$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
▲ 0
Correct answer: (a) $\frac{56}{33}$
$\tan(\alpha+\beta)=\frac34$, $\tan(\alpha-\beta)=\frac5{12}$; $\tan2\alpha=\tan((\alpha+\beta)+(\alpha-\beta))=\frac{\frac34+\frac5{12}}{1-\frac34\cdot\frac5{12}}=\frac{56}{33}$.
JEE Main 2010 · Trigonometry — verified solution by the Vidaara Team.
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