What is the general solution for 1+cos^2(x)-2cos^2(x/2)=0 ?

The general solution for 1+cos^2(x)-2cos^2(x/2)=0 is x=2pin,x= pi/2+2pin,x=(3pi)/2+2pin

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1+cos^2(x)-2cos^2(x/2)=0

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

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

Solution steps

1 + cos^{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 = 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

2 cos^{2} (x) + 5 sin (x) = 5

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

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

cos (x) + sin (x - 1) = 0

sin^{22} (x) = \frac{1}{2}

What is the general solution for 1+cos^2(x)-2cos^2(x/2)=0 ?
The general solution for 1+cos^2(x)-2cos^2(x/2)=0 is x=2pin,x= pi/2+2pin,x=(3pi)/2+2pin