Chapter 5, Problem 4RE

To determine

To Name : The trigonometric function which is equivalent to $\sqrt{{\cot }^{2}x+1}$

Answer to Problem 4RE

The function which is equivalent to $\sqrt{{\cot }^{2}x+1}$ is $\csc x$ .

Explanation of Solution

Given information:

  $\sqrt{{\cot }^{2}x+1}$

Concept and Formula Used:

  $1+{\cot }^{2}x={\csc }^{2}x$

Calculation:

The given trigonometric expression is

  $\sqrt{{\cot }^{2}x+1}$

As, $1+{\cot }^{2}x={\csc }^{2}x$ so we have $\sqrt{1+{\cot }^{2}x}=\sqrt{{\csc }^{2}x}=\csc x$ .

The function which is equivalent to $\sqrt{{\cot }^{2}x+1}$ is $\csc x$

Conclusion:

The function which is equivalent to $\sqrt{{\cot }^{2}x+1}$ is $\csc x$ .