Question

$sin{163}^{\circ }cos{347}^{\circ }+sin{73}^{\circ }sin{167}^{\circ }=$

• A. 0
• B. $\frac{1}{2}$
• C. 1
• D. None of these

Answer 1

The correct option is B

$\frac{1}{2}$

$sin{163}^{\circ }cos{347}^{\circ }+sin{73}^{\circ }sin{167}^{\circ }==sin({180}^{\circ }-{17}^{\circ })cos({360}^{\circ }-{13}^{\circ })+sin({90}^{\circ }-{17}^{\circ })sin({180}^{\circ }-{13}^{\circ })=sin{17}^{\circ }cos{13}^{\circ }+cos{17}^{\circ }sin{13}^{\circ }=sin({17}^{\circ }+{13}^{\circ })\left[sin\right(A+B)=sinAcosB+sinBcosA]=sin{30}^{\circ }\frac{1}{2}$