Question

If Tan⁴θ + Tan²θ = 1, then what is the value of Cos⁴θ + Cos²θ?

1. 8
2. 10
3. 1
4. 2

Answer 1

Correct Answer - Option 3 : 1

Given:

Tan4θ + Tan2θ = 1

Formula:

Sec²θ - Tan²θ = 1

Sin² θ + Cos²θ = 1

Calculation:

Tan4θ + Tan2θ = 1

⇒ Tan²θ (Tan²θ + 1) = 1

⇒ Tan²θ. Sec²θ = 1      {∵ sec²θ = 1 + tan²θ}

⇒ (sin² θ/cos⁴ θ) = 1

⇒ 1 – cos²θ = cos⁴ θ      {∵ sin² θ = 1 – cos²θ}

⇒ cos⁴ θ + cos² θ = 1

∴ Then the value of cos⁴ θ + cos² θ is 1.