163^ 347^ + 73^ 167^ = - Vidyadip

MCQ

$\sin163^\circ\cos347^\circ+\sin73^\circ\sin167^\circ=$

A
$0$
✓
$\frac{1}{2}$
C
$1$
D
None of these

✓

Answer

Correct option: B.

$\frac{1}{2}$

$\sin163^\circ\cos347^\circ+\sin73^\circ\sin167^\circ$
$=\ \sin(180^\circ-17^\circ)\cos(360^\circ-13^\circ)\\ \ \ +\sin(90^\circ-17^\circ)\sin(180^\circ+13^\circ)$
$=\ \sin17^\circ\cos13^\circ+\cos17^\circ\sin13^\circ$
$=\ \sin(17^\circ+13^\circ)$ $[\sin(\text{A+B})=\sin\text{A}\cos\text{B}+\sin\text{B}\cos\text{A}]$
$=\ \sin30^\circ$
$=\ \frac{1}{2}$

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