Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If tan3θ.tan7θ= 1, where 7θ is an acute angle, then find the value of cot15θ.

Options:

-1

-$\sqrt{3}$

$\sqrt{3}$

Correct Answer:

-1

Explanation:

tan3θ.tan7θ= 1

tan3θ = $\frac{1}{tan7θ}$

tan3θ = cot7θ

tan3θ = tan(90 - 7θ)

Thus, 3θ = 90 - 7θ

10θ = 90 or θ = 9

cot15θ = cot135 = -1