If cot67θ + tan133θ = 2, fin

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If cot⁶⁷θ + tan¹³³θ = 2, find sin2θ + 2cosθ.

Options:

√2 + 1

√2 - 1

1 + √2

1 - √2

Correct Answer:

1 + √2

Explanation:

If cotⁿθ + tanⁿθ = 2 then cotθ = tanθ = 1 where θ = 45°

Now,

⇒ sin2θ + 2cosθ = 1 + 2 × (\(\frac{1}{√2}\))

= 1 + √2