Question

If $\csc \theta +\cot \theta =5$, then $\csc \theta -\cot \theta =$

• A. $5$
• B. $\frac{1}{5}$
• C. $1$
• D. ${\csc }^2\theta -{\cos }^2\theta$

Answer 1

The correct option is B $\frac{1}{5}$

Given $\text{csc}\theta +\cot \theta =5$

As we know that

${\text{csc}}^2\theta -{\cot }^2\theta =1$

$⟹(\text{csc}\theta -\cot \theta )(\text{csc}\theta +\cot \theta )=1$

$⟹\text{csc}\theta -\cot \theta =\frac{1}{\text{csc}\theta +\cot \theta }=\frac{1}{5}$