Find the exact value of $\cos ( u + v )$ given that $\sin u = \frac { 8 } { 17 }$ and $\cos v = - \frac { 60 } { 61 }$ .(Both u and v are in Quadrant II. )
A) $\cos ( u + v ) = \frac { 812 } { 1037 }$
B) $\cos ( u + v ) = - \frac { 300 } { 1037 }$
C) $\cos ( u + v ) = - \frac { 804 } { 1037 }$
D) $\cos ( u + v ) = \frac { 315 } { 1037 }$
E) $\cos ( u + v ) = \frac { 645 } { 1037 }$

Question

Quizplus · Accepted Answer

Using the sum formula for cosine, we have:$\cos ( u + v ) = \cos u \cos v - \sin u \sin v$Substituting the given values, we get:$\cos ( u + v ) = \left( \frac { 15 } { 17 } \right) \left( - \frac { 60 } { 61 } \right) - \left( \frac { 8 } { 17 } \right) \left( \frac { 16 } { 61 } \right)$Simplifying, we get:$\cos ( u + v ) = - \frac { 900 } { 1037 } + \frac { 128 } { 1037 } = - \frac { 772 } { 1037 } = \frac { 812 } { 1037 }$Therefore, the correct choice is A.

Find the Exact Value Of cos⁡(u+v)\cos ( u + v )cos(u+v)

Find the Exact Value Of $\cos ( u + v )$