Question

If $\sin$$\theta =\frac{1}{3}$, then the value of $2{\cot }^2\theta +2$ is:

• A. $6$
• B. $9$
• C. $18$
• D. $4$

Answer 1

Answer: (C)

$18$

$\sin \theta =\frac{1}{3}$

$\Rightarrow {\sin }^2\theta =\frac{1}{9}$

$\Rightarrow {\cos }^2\theta =1-{\sin }^2\theta =1-\frac{1}{9}=\frac{8}{9}$

$\Rightarrow 2{\cot }^2\theta +2=2.\frac{{\cos }^2\theta }{{\sin }^2\theta }+2$

$=2\frac{\left(\frac{8}{9}\right)}{\left(\frac{1}{9}\right)}+2$

$=16+2$

$=18$

Hence, the answer is $18.$