What is the general solution for cos(x)-sqrt(cos(x))=0 ?

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

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cos(x)-sqrt(cos(x))=0

cos (x) - cos (x) = 0

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

Solution steps

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

3 cos (x) - 2 = 1

sin (4 x) = - sin (2 x)

t, x = 1 - 2 cos (2 t)

x, sin (3 x) = - \frac{3}{2}

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