Question

Given:
cos u = 3/5; 0 < u < pi/2
cos v = 5/13; 3pi/2 < v < 2pi

Find:
sin (v + u)
cos (v - u)
tan (v + u)

First compute or list the cosine and sine of both u and v.

Then use the combination rules
sin (v + u) = sin u cos v + cos v sin u.
cos (v - u) = cos u cos v + sin u sin v
and
tan (u + v) = [tan u + tan v]/[1 - tan u tan v]

We got sin u = 4/5 & sin v = SQRT (7/13)

Answer 1

if cos u=3/5
cos v=5/13
then sin u=4/5 and sin v=12/13
then sin(v+u)=sinv cos u+cos v sin u
sin(v+u)=56/65
cos(v-u)=63/65
Tan u=4/3 and tan v=12/5 then
tan(u+v)=-56/33