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Mathematics

If 3 cos θ = 1, then the value of cosec θ is:

  1. 222\sqrt{2}

  2. (322)\Big(\dfrac{3}{2\sqrt{2}}\Big)

  3. (233)\Big(\dfrac{2\sqrt{3}}{3}\Big)

  4. (432)\Big(\dfrac{4}{3\sqrt{2}}\Big)

Trigonometric Identities

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Answer

Given,

3 cos θ = 1

We know that,

⇒ sin2 θ = 1 - cos2 θ

⇒sin⁡2θ=1−19⇒sin⁡2θ=9−19⇒sin⁡2θ=89⇒sin⁡θ=223⇒cosec⁡θ=1sin⁡θ=322.\Rightarrow \sin^2 \theta = 1 - \dfrac{1}{9} \\[1em] \Rightarrow \sin^2 \theta = \dfrac{9 - 1}{9} \\[1em] \Rightarrow \sin^2 \theta = \dfrac{8}{9} \\[1em] \Rightarrow \sin \theta = \dfrac{2\sqrt{2}}{3} \\[1em] \Rightarrow \cosec \theta = \dfrac{1}{\sin \theta} = \dfrac{3}{2\sqrt{2}}.

Hence, option 2 is the correct option.

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