Question

The value of $\sin (A+B)$ if $\sin A=\frac{3}{5}$ and $cosB=\frac{8}{17}$ is $\frac{84}{85}$

• A. True
• B. False

Answer 1

The correct option is A True

$\sin A=\frac{3}{5}⟹\cos A=\frac{4}{5}$

$\cos B=\frac{8}{17}⟹\sin B=\frac{15}{17}$

$\sin (A+B)=\sin A\cos B+\cos A\sin B$

$\Rightarrow \frac{3}{5}\times \frac{8}{17}+\frac{4}{5}\times \frac{15}{17}$

$\Rightarrow \frac{24+60}{85}=\frac{84}{85}$