Question

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

Answer 1

$\left(\frac{sin{25}^{\circ }}{sec{65}^{\circ }}\right)+\left(\frac{cos{25}^{\circ }}{cosec{65}^{\circ }}\right)=sin{25}^{\circ }cos{65}^{\circ }+cos{25}^{\circ }sin{65}^{\circ }$

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

$=sin{25}^{\circ }sin{25}^{\circ }+cos{25}^{\circ }cos{25}^{\circ }$

$=si{n}^2{25}^{\circ }+co{s}^2{25}^{\circ }=1$