Question

The value of $\frac{\cos {80}^o}{\sin {10}^o}+\frac{\cos {59}^o}{\sin {31}^o}$ is :

• A. 1
• B. 2
• C. 0
• D. 3

Answer 1

The correct option is B 2

The value of $\frac{\cos {80}^o}{\sin {10}^o}+\frac{\cos {59}^o}{\sin {31}^o}$ is
$=\frac{\cos ({90}^o-{10}^o)}{\sin {10}^o}+\frac{\cos ({90}^o-{31}^o)}{\sin {31}^o}$ .....$\left[\cos ({90}^o-\theta )=\sin \theta \right]$
$=\frac{\sin {10}^o}{\sin {10}^o}+\frac{\sin {31}^o}{\sin {31}^o}$

$=1+1=2$