Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

Simplify. $\frac{cos^4 θ−sin^4 θ}{sin^2 θ}$

Options:

$1 − tan^2 θ$

$tan^ 2 θ − 1$

$cot^ 2 θ − 1$

$1 − cot^2 θ$

Correct Answer:

$cot^ 2 θ − 1$

Explanation:

$\frac{cos^4 θ−sin^4 θ}{sin^2 θ}$

= \(\frac{( cos²θ - sin²θ ) . ( cos²θ + sin²θ ) }{sin²θ}\)

{ using , cos²θ + sin²θ = 1 }

= \(\frac{( cos²θ - sin²θ ) . 1  }{sin²θ}\)

= \(\frac{( cos²θ  }{sin²θ}\) - \(\frac{( sin²θ  }{sin²θ}\)

= cot²θ - 1