Question:
sin 163° cos 347° + sin 73° sin 167° =
(a) 0
(b) $\frac{1}{2}$
(c) 1
(d) None of these
Solution:
(b) $\frac{1}{2}$
$\sin 163^{\circ} \cos 347^{\circ}+\sin 73^{\circ} \sin 167^{\circ}$
$=\sin \left(180^{\circ}-17^{\circ}\right) \cos \left(360^{\circ}-13^{\circ}\right)+\sin \left(90^{\circ}-17^{\circ}\right) \sin \left(180^{\circ}-13^{\circ}\right)$
$=\sin 17^{\circ} \cos 13^{\circ}+\cos 17^{\circ} \sin 13^{\circ}$
$=\sin \left(17^{\circ}+13^{\circ}\right)$ $[\sin (A+B)=\sin A \cos B+\sin B \cos A]$
$=\sin 30^{\circ}$
$=\frac{1}{2}$
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