Question

If$\sin \theta =\frac{1}{5}$, then, the value of $\frac{1}{5}{\cot }^2\theta +\frac{1}{5}$ is equal to:

• A. $\frac{1}{125}$
• B. $\frac{1}{5}$
• C. $25$
• D. $5$

Answer 1

Answer: (D)

$5$

we can write, $\text{cosec}\theta =5$

and

${\cot }^2\theta ={\text{cosec}}^2\theta -1\Rightarrow {\cot }^2\theta =25-1=24$

Now, $\frac{1}{5}{\cot }^2\theta +\frac{1}{5}=\frac{24}{5}+\frac{1}{5}=5$

Therefore, Answer is $5$