Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If $1 + tan θ = \sqrt{3}$, then $\sqrt{3} cot θ -1$ = _________.

Options:

$\frac{\sqrt{3}+1}{2}$

$\frac{\sqrt{3}-1}{2}$

$\frac{2\sqrt{3}-1}{2}$

$\frac{2\sqrt{3}+1}{2}$

Correct Answer:

$\frac{\sqrt{3}+1}{2}$

Explanation:

1 + tan θ = √3

tan θ = √3- 1

Now,

√3.cotθ - 1

= √3 ×  \(\frac{1}{√3- 1 }\) - 1 

= √3 ×  \(\frac{√3+ 1}{2 }\) - 1  

= \(\frac{√3+ 1}{2 }\)