If $sin^4x + sin^2x = 1$, then what is t

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If $sin^4x + sin^2x = 1$, then what is the value of $cot^4x + cot^2x$ ?

Options:

-2

-1

Correct Answer:

Explanation:

We are given that,

$sin^4x + sin^2x = 1$

$sin^4x = 1 - sin^2x$

{ we know, sin²x + cos²x = 1 }

$sin^4x = cos^2x$

sin²x = $\frac{cos²x}{sin²x}$

sin²x = cot²x -----(1)

Now,

$cot^4x + cot^2x$

By using equation 1.

= sin⁴ x + sin²x

= 1 { given }