Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

The expression $(cos^6\theta +sin^6\theta -1) (tan^2\theta +cot^2\theta +2)+1$ is equal to :

Options:

1

-2

0

-1

Correct Answer:

-2

Explanation:

(cos6θ + sin6θ - 1 ) ( tan2θ + cot2θ + 2 ) + 1

Put θ = 30º

= (  (\(\frac{√3}{2}\))6 + (\(\frac{1}{2}\))6 - 1 ) ( (\(\frac{1}{√3}\))2 + (√3)2 + 2 ) + 1

= ( \(\frac{27}{64}\) + \(\frac{1}{64}\) - 1 ) ( \(\frac{1}{3}\) + 3 + 2 ) + 1

= ( -\(\frac{36}{64}\)  ) ( \(\frac{16}{3}\)  + 1

= -2