If tan (\(\frac{π}{2}\) - 3θ) =

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If tan (\(\frac{π}{2}\) - 3θ) = \(\frac{1}{√3}\) , the value of cos3θ is?

Options:

-\(\frac{1}{2}\)

\(\frac{1}{2}\)

Correct Answer:

\(\frac{1}{2}\)

Explanation:

tan (\(\frac{π}{2}\) - 3θ) = \(\frac{1}{√3}\)

⇒ tan (\(\frac{π}{2}\) - 3θ) = tan 30°

⇒ 90 - 3θ = 30°

⇒ 3θ = 60° ⇒ θ = 20°

cos 3θ = cos 60° = \(\frac{1}{2}\)