find cos (u+v) when cos v=(1/3) and sin u=(2/5)
I found sin (v) to equal (sqrt8)/3
and cos (u)= (sqrt21)/5
Your values of sinv and cosu are correct.
v = 70.529 degrees
u = 23.578 degrees
u+v = 94.107 degrees
cos(u+v) = -0.07162
To get cos(u +v), use the identity
cos(u+v) = cosu*cosv - sinu*sinv
= sqrt21/5*(1/3) - (2/5)*sqrt8/3
= (1/15)*[sqrt21 - 2sqrt8)
(This is the exact value)
= -0.07162 (approximately)