What is the general solution for sin^2(x)=2-2cos(x) ?

The general solution for sin^2(x)=2-2cos(x) is x=2pin

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sin^2(x)=2-2cos(x)

sin^{2} (x) = 2 - 2 cos (x)

x = 2 πn

Solution steps

sin^{2} (x) = 2 - 2 cos (x)

Subtract

2 - 2 cos (x)

from both sides

sin^{2} (x) - 2 + 2 cos (x) = 0

Rewrite using trig identities

- 1 - cos^{2} (x) + 2 cos (x) = 0

Solve by substitution

cos (x) = 1

cos (x) = 1 : x = 2 πn

Combine all the solutions

x = 2 πn

4 sin (θ) - 3 = 0

cos (3 θ) = 0

2 sin (θ) + 4 = 3

sin^{2} (x) - sin (x) = cos^{2} (x)

tan (θ) = - \frac{3}{4}

What is the general solution for sin^2(x)=2-2cos(x) ?
The general solution for sin^2(x)=2-2cos(x) is x=2pin