Question

If sin θ + sin² θ = 1, then cos² θ + cos⁴ θ = 

Options

• −1

• 1

• 0 

• None of these

Answer 1

Given: 

`sin θ+sin^2θ=1` 

`⇒ 1-sin^2θ= sin θ`

Now,

`cos^2θ+cos^4θ`  

`= cos^2 θ+cos^2θcos^2θ`

=` cos^2θ+(1-sin^2θ)(1-sin^2θ)`

`=cos^2θ+sinθ sinθ`

`=cos^2 θ+sin^2θ`

`=1`