Question

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

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

Answer 1

The correct option is B

0

$sin{50}^{\circ }-sin{70}^{\circ }+sin{10}^{\circ }=2sin\left(\frac{{50}^{\circ }-{70}^{\circ }}{2}\right)cos\left(\frac{{50}^{\circ }+{70}^{\circ }}{2}\right)+sin{10}^{\circ }[\because sinA-sinB=2sin\left(\frac{A-B}{2}\right)cos\left(\frac{A+B}{2}\right)]=2sin(-{10}^{\circ })cos{60}^{\circ }+sin{10}^{\circ }=2\times \frac{1}{2}sin(-{10}^{\circ })+sin{10}^{\circ }=-sin{10}^{\circ }+sin{10}^{\circ }=0$