Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

The value of $\sin ^2 60^{\circ} \cos ^2 45^{\circ}+2 \tan ^2 60^{\circ}-{cosec}^2 30^{\circ}$ is equal to:

Options:

$\frac{17}{24}$

$\frac{19}{8}$

$-\frac{17}{24}$

$-\frac{19}{8}$

Correct Answer:

$\frac{19}{8}$

Explanation:

sin²60º . cos²45º + 2 tan²60º - cosec²30º

= \(\frac{3}{4}\) ×  \(\frac{1}{2}\) + 2 × 3 - 4

= \(\frac{3}{8}\)  + 2

= \(\frac{19}{8}\)