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

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

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

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

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

Solution steps

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

4 sin^{4} (x) + 12 cos^{2} (x) - 7 = 0

5 sin (a) = 4

2 cos^{4} (x) + 8 sin^{2} (x) = 5

cos^{4} (a) + cos^{2} (a) = 1

1 - cos (x) = 2 + cos (x)

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