Question

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

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

Answer 1

The correct option is C $\frac{24}{25}$

$\sin \alpha =\frac{3}{5},$ $\cos \beta =\frac{4}{5}$

$\cos \alpha =\frac{4}{5},$ $\sin \beta =\frac{3}{5}$

$\sin (\alpha +\beta )=\sin \alpha \cos \beta +\cos \alpha \sin \beta$

$=(\frac{3}{5}\times \frac{4}{5})+(\frac{4}{5}\times \frac{3}{5})$

$=\frac{12}{25}+\frac{12}{25}$

$=\frac{24}{25}$