Question

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

• A. 1
• B. 0
• C. -1
• D. none of these

Answer 1

The correct option is B 0

Using $sin\alpha +sin(\alpha +\beta )+sin(\alpha +2\beta )+.....sin(\alpha +\overline{n-1}\beta )=\frac{sin\frac{n\beta }{2}}{sin\frac{\beta }{2}}sin(\alpha +\frac{n-1}{2}\beta )$
We get
$sin{10}^o+sin{20}^o+sin{30}^o+.....+sin{360}^o=\frac{sin\frac{35\times {10}^o}{2}}{sin\frac{{10}^o}{2}}sin({10}^o+\frac{35-1}{2}{10}^o)$

$=\frac{sin{175}^o}{sin{5}^o}sin({10}^o+{170}^o)=\frac{sin(\pi -5^o)}{sin{5}^o}\cdot sin{180}^o=0$