Question

Find the value of the following:-
(a) $\frac{sin{31}^{\circ }}{2cos{59}^{\circ }}$
(b) $\frac{sec{70}^{\circ }}{2cosec{20}^{\circ }}+\frac{sin{59}^{\circ }}{cos{31}^{\circ }}$

Answer 1

a.$\frac{\sin 31°}{2\cos 59°}=\frac{\sin 31°}{2\cos (90°-31°)}=\frac{\sin 31°}{2\sin 31°}$

$=\frac{1}{2}$

b. $\frac{\sec 70°}{2\csc 20°}+\frac{\sin 59°}{\cos 31°}$

$\frac{\sec 70°}{2\csc (90°-70°)}+\frac{\sin 59°}{\cos (90°-59°)}$

$=\frac{\sec 70°}{2\sec 70°}+\frac{\sin 59°}{\sin 59°}$

$=\frac{1}{2}+1=\frac{3}{2}$