Cos (a+b) sin a=-3/5 sin b=-5/13 a & b in Q3 ?
$$\boxed{\cos(a+b)=\;?} \quad \sin{(a)} =-{3\over5} \qquad \sin {(b)}=-{5\over13}$$
$$\cos{(a+b)}=\cos{(a)}*\cos(b)-sin{(a)}*\sin{(b)}$$
cos(a)=? and cos(b)=?
$$\textstyle{
\cos{(a)}=\sqrt{1-\sin^2{(a)}}=
\sqrt{1-({3\over5})^2}= {\sqrt{5^2-3^2}\over5}={\sqrt{16}\over5}={\pm4\over5}=\pm{4\over5}
}$$
$$\textstyle{
\cos{(b)}=\sqrt{1-\sin^2{(b)}}=
\sqrt{1-({5\over13})^2}= {\sqrt{13^2-5^2}\over13}={\sqrt{144}\over13}={\pm12\over13}=\pm{12\over13}
}$$
$$\cos{(a+b)}=\pm
({4\over5})
\times
({12\over13})
-
(-{3\over5})
\times
(-{5\over13})$$
$$\cos{(a+b)}=\pm
({4\over5})
\times
({12\over13})
-
({3\over5})
\times
({5\over13})$$
$$\cos{(a+b)}=({\pm(4*12)\over5*13})
-
({3*5\over5*13})$$
$$\cos{(a+b)}={\pm(4*12)-3*5\over5*13}$$
$$\cos{(a+b)}={\pm48-15\over65}$$
$$\text{1.) }\cos{(a+b)}={48-15\over65}={33\over65}=0.50769230769$$
$$\text{2.) }\cos{(a+b)}={-48-15\over65}=-{63\over65}=-0.96923076923$$
.
