What condition is sin α = 1 / 2 for Cos2 α = 1 / 2 Is it unnecessary? How to push?

What condition is sin α = 1 / 2 for Cos2 α = 1 / 2 Is it unnecessary? How to push?

cos2α =1 -2(sinα)^2
= 1 - 2 *1/4
=1/2
From "Cos2 α = 1 / 2", sin α = 1 / 2 or - 1 / 2 is deduced
cos2α =1 -2(sinα)^2 =1/2
(sinα)^2=1/4
Sin α = 1 / 2 or - 1 / 2

Given sin θ 2 + cos θ 2 = 12, then cos 2 θ=______ ．

Because sin θ 2 + cos θ 2 = 12, so (sin θ 2 + cos θ 2) 2 = 14, ｜ sin θ = - 34, Cos2 θ = 1-2sin2 θ = 1-2 × (− 34) 2 = - 18

If Cos2 ^ (α / 2): sin α = 1:2, then Tan (α / 2)

cos2^(α/2):sinα=1:2
That is sin α = 2cos & # 178; (α / 2)
That is, 2Sin (α / 2) cos (α / 2) = 2cos & # 178; (α / 2)
That is sin (α / 2) = cos (α / 2)
∴ tan(α/2)=1

How to find sin square x + (2-cos) square

sin²x+(2-cosx)²
=sin²x+4-4cosx+cos²x
=1+4-4cosx
=5-4cosx