What is the general solution for 4cos^3(x)=4cos(x) ?

The general solution for 4cos^3(x)=4cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x=pi+2pin,x=2pin

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4cos^3(x)=4cos(x)

4 cos^{3} (x) = 4 cos (x)

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

Solution steps

4 cos^{3} (x) = 4 cos (x)

Solve by substitution

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

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

cos (x) = - 1 : x = π + 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 = π + 2 πn, x = 2 πn

sec (x) = \frac{5}{4}

sin (x) tan (x) = - 9 tan (x)

cos (x) - cos (3 x) = 0

5 cos (x) tan (x) + 3 tan (x) = 0

2 sec (θ) + 2 = 6

What is the general solution for 4cos^3(x)=4cos(x) ?
The general solution for 4cos^3(x)=4cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x=pi+2pin,x=2pin