Question

The value of $\sin {10}^o+\sin {20}^o+\sin {30}^o+........+\sin {360}^o$ is equal to-

• A. 0
• B. 1
• C. $sqrt3$
• D. 2

Answer 1

The correct option is A 0

$\sin {10}^o+\sin {20}^o+\sin {30}^o+........+\sin {360}^o=\sin {10}^o+\sin (10+10)+\sin (10+2\times 10)+........+\sin (10+35\times 10)$
$=\frac{\sin \left(\frac{36\times 10}{2}\right)}{\sin \left(\frac{10}{2}\right)}\sin (10+\frac{35\times 10}{2})=0$