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

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

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

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

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

Solution steps

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

Subtract

2 cos^{2} (\frac{x}{2})

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

cos (x) = - 1 : x = π + 2 πn

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

Combine all the solutions

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

- cos (a) - 11 = 2 cos (a) - 9

4 - 2 sin (x) = 0

sin^{2} (θ) - 2 sin (θ) + 3 = 0

3 tan^{2} (θ) + 3 tan (θ) = 0, 0^{\circ} \leq θ \leq 36 0^{\circ}

cos (a) = \frac{24}{25}

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