Cos^2x-10sinx+10=0

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Cos^2x-10sinx+10=0

Cos^2x = 1 - Sin^2x

1 - Sin^2x - 10Sinx + 10 = 0

-Sin^2x - 10Sinx + 11 = 0

t = Sinx ∈ [-1; 1]

-t^2 - 10t + 11 = 0

D = 100 - 4 * (-1) * 11 = 144

t1 = (10 + √144) / - 2 = - 11 ∉ [-1; 1]

t2 = (10 - √144) / - 2 = 1

Sinx = 1 = > x = π/2 + 2πn, n ∈ Z