Question

Find the value of:

$\sin {60}^{\circ }\cos {30}^{\circ }+\cos {60}^{\circ }\cdot \sin {30}^{\circ }$

Answer 1

To prove: $\sin {60}^{\circ }cos{30}^{\circ }+cos{60}^{\circ }\cdot \sin {30}^{\circ }=1$
L.H.S.: $\sin {60}^{\circ }\cos {30}^{\circ }+\cos {60}^{\circ }\cdot \sin {30}^{\circ }$

= $\left(\frac{\sqrt{3}}{2}\right)\left(\frac{\sqrt{3}}{2}\right)+\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)$

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