Question

Evaluate: $\sin {25}^{\circ }\cos {65}^{\circ }+\cos {25}^{\circ }\sin {65}^{\circ }$

• A. 0
• B. 1
• C. -1
• D. $\sqrt{2}$

Answer 1

The correct option is B 1

$\sin {25}^{\circ }\cos {65}^{\circ }+\cos {25}^{\circ }\sin {65}^{\circ }$
$=\sin {25}^{\circ }\sin ({90}^{\circ }-{65}^{\circ })+\cos {25}^{\circ }\cos ({90}^{\circ }-{65}^{\circ })$
$=\sin {25}^{\circ }\sin {25}^{\circ }+\cos {25}^{\circ }\cos {25}^{\circ }$
$={\sin }^2{25}^{\circ }+{\cos }^2{25}^{\circ }$
$=1$