Question

$\sin {50}^{\circ }-\sin {70}^{\circ }+\sin {10}^{\circ }=$

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

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