Question

State whether true or false.

$\sin \frac{8\pi }{3}\cos \frac{23\pi }{6}+\cos \frac{13\pi }{3}\sin \frac{35\pi }{6}=\frac{1}{2}$

• A. True
• B. False

Answer 1

The correct option is A True

$\sin \frac{8\pi }{3}\cos \frac{23\pi }{6}+\cos \frac{13\pi }{3}\sin \frac{35\pi }{6}$

$=\sin (3\pi -\frac{\pi }{3})\cos (4\pi -\frac{\pi }{6})+\cos (4\pi +\frac{\pi }{3})\sin (6\pi -\frac{\pi }{6})$

$=\sin \frac{\pi }{3}\cos \frac{\pi }{6}-\cos \frac{\pi }{3}\sin \frac{\pi }{6}$

$=\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}-\frac{1}{2}\times \frac{1}{2}$

$=\frac{3-1}{4}=\frac{2}{4}=\frac{1}{2}$

Hence the given statement is true.