Question

Simplify the expression (Picture provided)

Answer 1

Answer:

$\sec(\theta)$

Step-by-step explanation:

We want to simplify

$\frac{\csc(\theta)}{\cot(\theta)}$

We express in terms of the sine and cosine ratios to obtain;

$\frac{\frac{1}{\sin(\theta)} }{\frac{\cos(\theta)}{\sin(\theta)} }$

This is the same as

$\frac{1}{\sin(\theta)} \div \frac{\cos(\theta)}{\sin(\theta)}$

Multiply by the reciprocal to get;

$\frac{1}{\sin(\theta)} \times \frac{\sin(\theta)}{\cos(\theta)}$

Cancel the common factors;

$\frac{1}{\cos(\theta)}=\sec(\theta)$

Answer 2

Answer:

b.  secx

Step-by-step explanation:

We have given a trigonometric expression.

csc(x)/cot(x)

We have to simplify it.

Since we know that

csc(x) is reciprocal to sin(x).

cscx = 1/sinx

cot(x) is ratio of cos(x) and sin(x).

cotx = cosx/sinx

Then, given expression becomes,

$\frac{1/sinx}{cosx/sinx}$

$\frac{1}{sinx}$ × $\frac{sinx}{cosx}$

$\frac{1}{cosx}$

csc(x)/cot(x)   = secx