Question

If sin A = $\frac{4}{5}$ and cos B = - $\frac{12}{13}$, where A and B lie in first

and third quadrant respectively, then cos(A + B) =

• A. $\frac{56}{65}$
• B. - $\frac{56}{65}$
• C. $\frac{16}{65}$
• D. - $\frac{16}{65}$

Answer 1

The correct option is D

- $\frac{16}{65}$

We have sin A = $\frac{4}{5}$ and cos B = - $\frac{12}{13}$

Now, cos(A + B) = cos A cos B - sin A sin B

= $\sqrt{1-\frac{16}{25}}$$(-\frac{12}{13})$ - $\frac{4}{5}$$(-\sqrt{1-\frac{144}{169}})$

= - $\frac{3}{5}$ × $\frac{12}{13}$ - $\frac{4}{5}$$(-\frac{5}{13})$ = - $\frac{16}{65}$

(Since A lies in first quadrant and B lies in third quadrant).