Question

Evaluate the following :
$\frac{\sec {70}^0}{\text{cosec}{20}^0}+\frac{\sin {59}^0}{\cos {31}^0}$

Answer 1

We have $\sec ({90}^0-\theta )=\csc \theta$ and $\sin ({90}^0-\theta )=\cos \theta$

therefore,

$\sec {70}^0=\sec ({90}^0-{20}^0)=\csc {20}^0$

$\sin {59}^0=\cos ({90}^0-{31}^0)=\cos {31}^0$

To evaluate,

$\frac{\sec {70}^0}{\csc {20}^0}+\frac{\sin {59}^0}{\cos {31}^0}$

$=\frac{\csc {20}^0}{\csc {20}^0}+\frac{\cos {31}^0}{\cos {31}^0}$

$=1+1$

$=2$