Question

If 3cos $\theta =$ 1, then the value of cosec $\theta$ is :

• A. $2\sqrt{2}$
• B. $\frac{3}{2\sqrt{2}}$
• C. $\frac{2\sqrt{3}}{3}$
• D. $\frac{4}{3\sqrt{2}}$

Answer 1

Answer: (B)

$\frac{3}{2\sqrt{2}}$

$3\cos \theta =1$

$\Rightarrow \cos \theta =\frac{1}{3}$

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

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

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

$\Rightarrow \sin \theta =\sqrt{\frac{8}{9}}$

$\Rightarrow \sin \theta =\frac{2\sqrt{2}}{3}$

$\Rightarrow cosec\theta =\frac{1}{\sin \theta }=\frac{3}{2\sqrt{2}}$

Hence, the answer is $\frac{3}{2\sqrt{2}}.$