Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

Find the value of $\frac{3}{4} \cot ^2 30^{\circ}+\cos ^2 30^{\circ}-3 cosec^2 60^{\circ}+\tan ^2 60^{\circ}$.

Options:

-4

10

$\frac{\sqrt{3}}{4}$

2

Correct Answer:

2

Explanation:

\(\frac{3}{4}\). cot²30º + cos²30º - 3 cosec²60º + tan²60º

= \(\frac{3}{4}\) × 3 + \(\frac{3}{4}\)  - 3 × \(\frac{4}{3}\) + 3

= \(\frac{9}{4}\) + \(\frac{3}{4}\)  - 4 + 3

= \(\frac{12}{4}\)  - 4 + 3

= 3 - 4 + 3

= 2