Question

If $\sin \alpha =\frac{3}{5}$ and $\cos \beta =\frac{4}{5}$,then the value of $\sin (\alpha +\beta )$

• A. $\frac{6}{25}$
• B. $\frac{12}{25}$
• C. $\frac{24}{25}$
• D. none of these

Answer 1

Answer: (C)

$\frac{24}{25}$

$\sin \alpha =\frac{3}{5},\cos \beta =\frac{4}{5}\sin (\alpha +\beta )=\sin \alpha \cos \beta +\cos \alpha \sin \beta =\frac{3}{5}\times \frac{4}{5}+\sqrt{1-{\sin }^2\alpha }\sqrt{1-{\cos }^2\beta }=\frac{12}{25}+\sqrt{1-\frac{9}{25}}\sqrt{1-\frac{16}{25}}=\frac{12}{25}+\frac{4}{5}\times \frac{3}{5}=\frac{12}{25}+\frac{12}{25}=\frac{24}{25}$