What is the general solution for cos(x)(cos(x)-1)=0 ?

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

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

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

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

Solution steps

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

Solving each part separately

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

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

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

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

cot (x) = 0

arccos (x) = 2 arccos (\frac{3}{4})

2 sin (x) - 3 = 0

2 cos^{2} (x) - 3 cos (x) + 1 = 0

sin (x) = cos (2 x)

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