Question

$\sin \left(\frac{5 \pi}{3}\right)+\sec \left(\frac{13 \pi}{3}\right)=$

• A. $2-\frac{\sqrt{3}}{2}$
• B. $2+\frac{\sqrt{3}}{2}$
• C. $\sqrt{3}+\frac{1}{\sqrt{2}}$
• D. $\sqrt{3}-\frac{1}{\sqrt{2}}$

Answer 1

Answer: (A)

$\sin \left(\frac{5 \pi}{3}\right)+\sec \left(\frac{13 \pi}{3}\right)$
$=\sin \left(2 \pi-\frac{\pi}{3}\right)+\sec \left(4 \pi+\frac{\pi}{3}\right)$
$=-\sin \frac{\pi}{3}+\sec \frac{\pi}{3}=-\frac{\sqrt{3}}{2}+2$
$=2-\frac{\sqrt{3}}{2}$