What is the general solution for 8cos^3(x)=8cos(x) ?

The general solution for 8cos^3(x)=8cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x=pi+2pin,x=2pin

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8cos^3(x)=8cos(x)

8 cos^{3} (x) = 8 cos (x)

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

Solution steps

8 cos^{3} (x) = 8 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 cos (2 θ) = cos^{2} (θ) - 2

2 cos^{2} (x) + sin (x) = 1, 0 \leq x \leq 2 π

cos (x) = \frac{5}{5}

4 sin (x) cos (x) = 2 sin (x)

(sec (t) - 2) (cot (t) + 1) = 0

What is the general solution for 8cos^3(x)=8cos(x) ?
The general solution for 8cos^3(x)=8cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x=pi+2pin,x=2pin