# Suppose that β is an acute angle and sec β = 11 . 3. How to do the following?

## (a) Find the exact value of: (i) cosec β, (ii) cot β. (b) Show that $c o$${\sec}^{2}$ β − ${\cot}^{2}$ β = 1.

May 19, 2018

cosec b = 1.0039
cot b = 0.0888

#### Explanation:

$\sec b = 11.3$ -->
$\cos b = \frac{1}{11.3} = 0.0885$. Find sin b.
${\sin}^{2} b = 1 - {\cos}^{2} b = 1 - 0.0078 = 0.9921$
$\sin b = 0.9960$
cosec b = $\frac{1}{\sin b} = 1.0039$
$\cot b = \cos \frac{b}{\sin b} = \frac{0.0085}{0.9960} = 0.0888$

$\cos e {c}^{2} b - {\cot}^{2} b = 1.0078 - 0.0078 = 1$. Proved