Question

Verify the given equalities.
$\sin {30}^{\circ }\cos {60}^{\circ }+\cos {30}^{\circ }\sin {60}^{\circ }=\sin {90}^{\circ }$

Answer 1

$\sin 30°\cos 60°+\cos 30°\sin 60°=\sin 90°$

$\Rightarrow L.H.S=\sin 30°\cos 60°+\cos 30°\sin 60°$

$=\frac{1}{2}\times \frac{1}{2}+\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}$

$=\frac{1}{4}+\frac{3}{4}$

$=\frac{4}{4}$

$=1$

$\Rightarrow R.H.S=\sin 90°=1$

$\therefore L.H.S=R.H.S$

Hence, answer verify.