Question

$2\sin^{2}\beta + 4\cos(\alpha + \beta)\sin\alpha\sin\beta + \cos 2(\alpha + \beta)$ equal to

• A. $\sin 2\alpha$
• B. $\cos 2\beta$
• C. $\tan A/2$
• D. $\sin 2\beta$

Answer 1

Answer: (C)

$\tan A/2$

Answer 2

Since $2\cos(\alpha + \beta) = 2\cos^{2}(\alpha + \beta) - 1,$

$2 \sin ^ { 2 } \beta = 1 - \cos 2 \beta$

$\sin A = \frac{4}{5}, = - \cos 2\beta + 2\cos(\alpha + \beta).\cos(\alpha - \beta) = - \cos 2\beta + \cos 2\alpha + \cos 2\beta = \cos 2\alpha$