Question

If $\sin ({60}^{\circ }+{30}^{\circ })$ = $\sin {60}^{\circ }\cos {30}^{\circ }+\sin {30}^{\circ }\cos {60}^{\circ }$ then what is the value of $\sin ({60}^{\circ }+{30}^{\circ }).$ =?

Answer 1

$sin{60}^0\cos {30}^0+sin{30}^0\cos {60}^0$

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

$=\left(\frac{3}{4}\right)+\left(\frac{1}{4}\right)=1$

$alsosin({60}^0+{30}^0)=sin{90}^0=1$