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

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

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

2 - 2 sin^{2} (\frac{x}{2}) = sin^{2} (x)

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

Solution steps

2 - 2 sin^{2} (\frac{x}{2}) = sin^{2} (x)

Subtract

sin^{2} (x)

from both sides

2 - 2 sin^{2} (\frac{x}{2}) - sin^{2} (x) = 0

Rewrite using trig identities

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

Solve by substitution

cos (x) = 0, cos (x) = - 1

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

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

sin (x) + cos (x) = 2

3 cos (B) - 1 = 5 cos (B) + 1

cos (θ) = \frac{3}{4}

cos (x) = \frac{- 3}{5}

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

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