Question

The value of $sin50^{\circ} - sin70^{\circ} + sin10^{\circ}$ is equal to

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

Answer 1

Answer: (B)

$0$

Answer 2

We have, $sin50^{\circ} - sin70^{\circ} + sin10^{\circ}$ $=\left(sin50^{\circ}+sin10^{\circ}\right)-sin70^{\circ}$ $=2sin\left(\frac{50+10}{2}\right)^{\circ}\,cos\left(\frac{50-10}{2}\right)^{\circ}-sin70^{\circ}$ $=2sin30^{\circ}\,cos20^{\circ}-sin70^{\circ}$ $=cos\left(90-70\right)^{\circ}-sin70^{\circ}$ $=sin70^{\circ}-sin70^{\circ}=0$