Question

If sin $\alpha$ = 5/13 and sin $\beta$ = $\frac{4}{5}$ then the value of cos $\alpha$ cos $\beta$ - sin $\alpha$ sin $\beta$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

5,12,13 are the sides of a right-angled $△$ and 3, 4, 5 are also sides of another right angled $△$

sin $\alpha$ = $\frac{5}{13}$; $\therefore$ cos $\alpha$ = $\frac{12}{13}$

sin $\beta$ = $\frac{5}{13}$; $\therefore$ cos $\beta$ = $\frac{3}{5}$

$\therefore$ cos $\alpha$ cos $\beta$ - sin $\alpha$ sin $\beta$ = $\left(\frac{12}{13}\right)\left(\frac{3}{5}\right)-\left(\frac{5}{13}\right)\left(\frac{4}{5}\right)$ = $\frac{36}{65}-\frac{20}{65}=\frac{16}{65}$