Question

cot⁴ θ + cot² θ is equal to ______.

Options

• 2 cot² θ. cosec² θ

• tan² θ + tan⁴ θ

• tan² θ.cosec² θ

• cosec⁴ θ − cosec² θ

Answer 1

cot⁴ θ + cot² θ is equal to cosec⁴ θ − cosec² θ.

Explanation:

Solving,

⇒ cot⁴ θ + cot² θ

⇒ cot² θ(cot² θ + 1)

⇒ cot² θ.cosec² θ

Substituting, cot² θ = cosec² θ - 1, we get :

⇒ (cosec² θ - 1).cosec² θ

⇒ cosec⁴ θ - cosec² θ.