Question

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

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

Answer 1

The correct option is D 5

$\sin \theta =\frac{1}{5}$

$\Rightarrow \frac{1}{5}{\cot }^2\theta +\frac{1}{5}=\frac{1}{5}[{\cot }^2\theta +1]$

$=\frac{cose{c}^2\theta }{5}$

$=\frac{1}{5{\sec }^2\theta }$

$=\frac{1}{5\times \frac{1}{25}}$

$=\frac{1}{\frac{1}{5}}$

$=5$

Hence, the answer is $5.$