Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

Is sinx - 3cosx = $\sqrt{3}$ cos x, then the value of cot x is  ___________.

Options:

$ 3 - \sqrt{3}$

$ 3 + \sqrt{3}$

$\sqrt{3}$

$\frac{3-\sqrt{3}}{6}$

Correct Answer:

$\frac{3-\sqrt{3}}{6}$

Explanation:

sinx - 3cox = √3 cosx

tanx - 3 = √3

tanx = 3 + √3 

cotx = \(\frac{1}{tanx}\)

= \(\frac{1}{3 + √3}\)

= \(\frac{1}{3 + √3}\)

= \(\frac{1}{3 + √3}\) ×  \(\frac{3 - √3}{3 - √3}\)

= \(\frac{3 - √3}{6}\)