If sin² θ = cos³ θ, then the value of (cot² θ - cot⁶ θ) is:

Question

Question

This question was previously asked in

SSC CPO 2022 Tier-I Official Paper (Held On 11 Nov 2022 Shift 2) [Answer Key]

Answer 1

Given:

sin2 θ = cos3 θ

Concept Used:

cosec2 θ – cot2 θ = 1

Calculation:

⇒ According to the question we have,

⇒ sin2 θ = cos3 θ

⇒ Squaring both sides

⇒ sin⁴ θ = cos⁶ θ ........(1)

⇒ Now,

⇒ cot2 θ - cot6 θ = cot2 θ – \(\frac{cos^6\theta}{sin^6\theta}\)

⇒ From equation 1

⇒ cot2 θ – \(\frac{sin^4\theta}{sin^6\theta}\) = cot2 θ – \(\frac{1}{sin^2\theta}\) = cot2 θ – cosec2 θ = –1

Therefore, the value of cot2 θ - cot6 θ is –1.

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