Question

If cos² θ + cos⁴ θ = 1, then the value of sin θ + sin² θ is:
1. 2
2. 1/2
3. 0
4. 1

Answer 1

Correct Answer - Option 4 : 1

Given data:

Cos² θ + cos⁴ θ = 1

Concept used:

Sin² θ + cos² θ = 1

Calculation:

Cos² θ + cos⁴ θ = 1

⇒ cos⁴ θ = 1 – cos² θ

∵ sin² θ = 1 – cos² θ

⇒ cos⁴ θ = sin² θ

Taking square roots of both the sides,

⇒ cos² θ = sin θ      ----(1)

Sin θ + sin² θ

⇒ cos² θ + sin² θ      ----(from equation 1)

⇒ 1

 

∴ The value of sin θ + sin² θ is 1.