Question

If sin x + sin² x = 1, then cos⁴ x + cos² x is equal to:

Answer 1

Correct Answer - Option 2 : 1

Concept:

• sin² θ + cos² θ = 1.
• (a ± b)² = a² ± 2ab + b².

 

Calculation:

We are given that sin x + sin2 x = 1.

⇒ sin x = 1 - sin2 x

⇒ sin x = cos2 x            ... (Using sin2 θ + cos2 θ = 1.)

⇒ sin² x =  cos4 x            ... (Squaring both sides.)

⇒ 1 - cos2 x = cos⁴ x            ... (Using sin2 θ + cos2 θ = 1.)

⇒ cos4 x + cos2 x = 1.