Question

sin 163° cos 347° + sin 73° sin 167° =
(a) 0

(b) $\frac{1}{2}$

(c) 1

(d) None of these

Answer 1

(b) $\frac{1}{2}$

$$\begin{gathered} \sin 163°\cos 347°+\sin 73°\sin 167° \\ =\sin \left(180°-17°\right)\cos \left(360°-13°\right)+\sin \left(90°-17°\right)\sin \left(180°-13°\right) \\ =\sin 17°\cos 13°+\cos 17°\sin 13° \\ =\sin \left(17°+13°\right)\left[\sin \left(A+B\right)=\sin A\cos B+\sin B\cos A\right] \\ =\sin 30° \\ =\frac{1}{2} \end{gathered}$$