Trigonometric Functions — MATHS STD 11 Science — Question

2. $\frac{1}{2}$

Solution:$$

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

$=\ \sin(180^\circ-17^\circ)\cos(360^\circ-13^\circ)\\ \ \ +\sin(90^\circ-17^\circ)\sin(180^\circ+13^\circ)$

$=\ \sin17^\circ\cos13^\circ+\cos17^\circ\sin13^\circ$

$=\ \sin(17^\circ+13^\circ)$ $[\sin(\text{A+B})=\sin\text{A}\cos\text{B}+\sin\text{B}\cos\text{A}]$

$=\ \sin30^\circ$

$=\ \frac{1}{2}$