Question

The value of $\frac{\cot {40}^o}{\tan {50}^o}-\frac{1}{2}\left(\frac{\cos {35}^o}{\sin {55}^o}\right)$ is

• A. 0
• B. 1
• C. $\frac{1}{2}$
• D. 2

Answer 1

The correct option is C $\frac{1}{2}$

The value of $\frac{\cot {40}^o}{\tan {50}^o}-\frac{1}{2}\left(\frac{\cos {35}^o}{\sin {55}^o}\right)$ is

$=\frac{\cot ({90}^o-{50}^o)}{\tan {50}^o}-\frac{1}{2}\left[\frac{\cos ({90}^o-{55}^o)}{\sin {55}^o}\right]$

$=\frac{\tan {50}^o}{\tan {50}^o}-\frac{1}{2}\left(\frac{\sin {55}^o}{\sin {55}^o}\right)$

$=1-\frac{1}{2}\times 1=\frac{1}{2}$