If sin θ + sin² θ = 1, then cos² θ + cos θ =
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Given:- sin θ + sin² θ = 1
To find:- cos² θ + cos⁴θ
Solution:-
sin θ + sin² θ = 1
[tex]\implies[tex] sin θ + 1-cos²θ = 1
[tex]\implies[tex] sinθ - cos²θ = 0
[tex]\implies[tex] sinθ = cos²θ
[tex]\implies[tex]sin²θ = cos⁴θ
[tex]\implies[tex]1-cos²θ = cos⁴θ
[tex]\implies[tex]cos⁴θ + cos²θ = 1
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