### Home > PC3 > Chapter 9 > Lesson 9.1.4 > Problem9-90

9-90.

Calculate the exact value of $\sec\left(a+b\right)$ where $cos(a) = \frac { 3 } { 5 }$, $a$ is in Quadrant IV, $\tan(b) = −\frac { 12 } { 5 }$, and $b$ is in Quadrant II. Hint: Calculate $\cos(a+b)$.

Sketch two triangles for this situation. One for angle $a$ and one for angle $b$.

$\cos(a + b) = \cos(a)\cos(b) − \sin(a)\sin(b)$