Question

If $\sin \alpha =\frac{4}{5}$ and $\cos \beta =\frac{12}{13}$, find $\sin \alpha \cos \beta +\cos \alpha \sin \beta$

• A. $\frac{63}{65}$
• B. $\frac{63}{67}$
• C. $\frac{61}{65}$
• D. $\frac{65}{63}$

Answer 1

The correct option is A $\frac{63}{65}$

$sin\alpha =\frac{4}{5}$
Hence
$cos\alpha =\frac{3}{5}$
Similarly
$cos\beta =\frac{12}{13}$
Hence
$sin\beta =\frac{5}{13}$
Substituting in the above expression, we get
$sin\alpha .cos\beta +cos\alpha .sin\beta$
$=\frac{48}{65}+\frac{25}{65}$
$=\frac{63}{65}$