Question

Prove that $\sin {80}^{\circ }\cos {10}^{\circ }$ + $\cos {80}^{\circ }sin{10}^{\circ }$ = 1

Answer 1

sin ${80}^{\circ }$ = sin (${90}^{\circ }-{10}^{\circ }$) = cos ${10}^{\circ }$

sin ${80}^{\circ }$ cos ${10}^{\circ }$ + cos ${80}^{\circ }$ sin ${10}^{\circ }$ = ( cos ${10}^{\circ }$ ) ( cos ${10}^{\circ }$ ) + ( sin ${10}^{\circ }$ ) ( sin ${10}^{\circ }$ )

= ${\cos }^2$ ${10}^{\circ }$ + ${\sin }^2$ ${10}^{\circ }$ = 1