Question

The value of $\frac{\cos {70}^o}{\sin {20}^o}+\frac{\cos {59}^o}{\sin {31}^o}-8{\sin }^2{30}^o$ is :

• A. $1$
• B. $2$
• C. $0$
• D. $3$

Answer 1

The correct option is C $0$

The value of $\frac{\cos {70}^o}{\sin {20}^o}+\frac{\cos {59}^o}{\sin {31}^o}-8{\sin }^2{30}^o$ is

$=\frac{\cos ({90}^o-{20}^o)}{\sin {20}^o}+\frac{\cos ({90}^o-{31}^o)}{\sin {31}^o}-{8\left(\frac{1}{2}\right)}^2$
$=\frac{\sin {20}^o}{\sin {20}^o}+\frac{\sin {31}^o}{\sin {31}^o}-8\times \frac{1}{4}$
$=1+1-2=0$