Question

The value of $\sin 30.\cos 60+\cos 30.\sin 60$ is

Answer 1

Use $sin({90}^{\circ }-\theta )=cos\theta$ and $cos({90}^{\circ }-\theta )=sin\theta$

and ${\cos }^2\theta +{\sin }^2\theta =1$

Now,

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

$=sin({90}^{\circ }-{60}^{\circ })\cdot cos{60}^{\circ }+cos({90}^{\circ }-{60}^{\circ })\cdot sin{60}^{\circ }$

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

$={\cos }^{2}60°+{\sin }^{2}60°=1$