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

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

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

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

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

Solution steps

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

Subtract

cos^{2} (x)

from both sides

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

Combine all the solutions

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

x, y sin (x y) = y^{2} + 2

3 sin (x) + 1 = 2 csc (x)

100 = (50) (40) cos (θ)

cos (x) = a

cos (4 w) = 0

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