What is the general solution for 4cos(x)=4cos(2x) ?

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

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

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

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

Solution steps

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

Subtract

4 cos (2 x)

from both sides

4 cos (x) - 4 cos (2 x) = 0

Rewrite using trig identities

- (- 1 + 2 cos^{2} (x)) \cdot 4 + 4 cos (x) = 0

Solve by substitution

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

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

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

cos (θ) = 513, 3 π^{2} < θ < 2 π

cos (x) + ∣ cos (x) ∣ = 1

2 sin (\frac{π}{3} - x) = 1

9 tan^{2} (z) cos (z) = 3 cos (z)

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

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