Question

If sinθ + sin² θ = 1, prove that cos² θ + cos⁴ θ = 1

Answer 1

We have,

`sinθ + sin^2 θ = 1`

`⇒ sinθ = 1 – sin^2 θ`

`⇒ sinθ = cos^2 θ`

Now, `cos^2 θ + cos^4 θ = cos^2 θ + (cos^2 θ)^2`

`= cos^2 θ + sin^2 θ = 1`