Question

If $\sin a=\frac{3}{5},\cos \beta =\frac{5}{13},$ then $\sin (a+\beta )$ is 63/65
If true then enter $1$ and if false then enter $0$

Answer 1

$\cos a=\sqrt{1-{\sin }^{2}a}=\sqrt{1-{\left(\frac{3}{5}\right)}^2}\Rightarrow \frac{4}{5}$
$\sin \beta =\sqrt{1-{\cos }^2\beta }=\sqrt{1-{\left(\frac{5}{13}\right)}^2}\Rightarrow \sin \beta =\frac{12}{13}$
Now, $\sin (a+\beta )=\sin a\cos \beta +\sin \beta cosa$
$=\frac{3}{5}\times \frac{5}{13}+\frac{4}{5}\times \frac{12}{13}$
$=\frac{15}{65}+\frac{48}{65}$
$=\frac{63}{65}$