Question

The value of $\sin {50}^{\circ }-\sin {70}^{\circ }+\sin {10}^{\circ }$ is

• A. $0$
• B. $1$
• C. $\frac{1}{2}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

The correct option is A $0$

$\sin {50}^{\circ }+\sin {10}^{\circ }-\sin {70}^{\circ }$
$=2\sin \left(\frac{{50}^{\circ }+{10}^{\circ }}{2}\right)\cos \left(\frac{{50}^{\circ }+{10}^{\circ }}{2}\right)-\sin ({90}^{\circ }-{20}^{\circ })$
$=2\sin {30}^{\circ }\cos {20}^{\circ }-\cos {20}^{\circ }$
$=\cos {20}^{\circ }(2\times \frac{1}{2}-1)=0$.