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

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

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

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

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

Solution steps

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

Subtract

sin^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

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

sin (θ) = \frac{2}{2}, 0 \leq θ \leq 2 π

x, cos (x) = \frac{2}{3}

3 sin (x) + 2 = 1.5

3 sec^{2} (x) - 2 tan (x) - 4 = 0

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

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