What is the general solution for 3cos(2x)=3cos(x) ?

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

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3cos(2x)=3cos(x)

3 cos (2 x) = 3 cos (x)

x = 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

3 cos (2 x) = 3 cos (x)

Subtract

3 cos (x)

from both sides

3 cos (2 x) - 3 cos (x) = 0

Rewrite using trig identities

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

Solve by substitution

cos (x) = 1, cos (x) = - \frac{1}{2}

cos (x) = 1 : x = 2 πn

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

sin^{2} (2 x) = 3 cos^{2} (2 x)

- 2 sin (θ) = 2 sin (2 θ)

cos (θ) = \frac{π}{2}

2 sin (4 x) + 3 = 0

sin (α) = 0

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