What is the general solution for 1-cos(x)=2-2sin^2(x) ?

The general solution for 1-cos(x)=2-2sin^2(x) is x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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

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

x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

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

Subtract

2 - 2 sin^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = - 1, cos (x) = \frac{1}{2}

cos (x) = - 1 : x = π + 2 πn

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

- 5 tan (x) - 12 = tan (x) - 8

5 = sec^{2} (x) + 3

sin (θ) = \frac{24}{25}

sin (2 t) = cos (t)

cos (2 x) + 1 = cos (x)

What is the general solution for 1-cos(x)=2-2sin^2(x) ?
The general solution for 1-cos(x)=2-2sin^2(x) is x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin