If , then:

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 3)

Answer 1

Given:

tan² θ + tan⁴ θ = 1

Concept used:

tan2 θ + 1 = sec² θ

Calculation:

⇒ tan2 θ + tan4 θ = 1

⇒ tan2 θ (1 + tan2 θ) = 1

⇒ tan2 θ × sec² θ = 1

⇒ tan2 θ = 1/sec² θ = cos² θ

Now put the value of tan2 θ in the equation:

⇒ tan2 θ + tan4 θ = 1

⇒ tan2 θ + (tan²)² θ = 1

⇒ cos2 θ + (cos²)² θ = 1

⇒ cos² θ + cos⁴ θ = 1

∴ The correct option is 2.

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