Question

If $\sin A = \frac{4}{5}$, then $(3 − \tan A)(2 + \cos A)$ is:

• A. $\frac{12}{5}$
• B. $\frac{13}{3}$
• C. $\frac{13}{5}$
• D. 3

Answer 1

Answer: (B)

$\frac{13}{3}$

Answer 2

Using $\sin A = \frac{4}{5}$, we calculate $\tan A = \frac{4}{3}$ and $\cos A = \frac{3}{5}$. Substituting into the expression gives $\left(3 − \frac{4}{3}\right)\left(2 + \frac{3}{5}\right) = \left(\frac{5}{3}\right) \times \left(\frac{13}{5}\right) = \frac{13}{3}$.