If cos^2 θ+cos^4θ=1, then the value of sinθ +sin^2θ is :

cos²θ + cos4θ = 1

cos4θ = 1 - cos²θ

{ using   sin²θ + cos²θ = 1 }

cos4θ = sin²θ

and cos²θ = sinθ

Now,

sinθ + sin²θ 

= cos²θ + cos4θ

= 1               { given :- cos²θ + cos4θ = 1 }