What is the general solution for cos(2x)*2-2cos(x)=0 ?

The general solution for cos(2x)*2-2cos(x)=0 is x=2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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

cos (2 x) \cdot 2 - 2 cos (x) = 0

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

Solution steps

cos (2 x) \cdot 2 - 2 cos (x) = 0

Rewrite using trig identities

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

- 2 sin (2 x) = \frac{π}{12}

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

sin (10 x) = sin (10 (x + 1))

sin^{2} (θ) + 3 sin (θ) = 0

cos (x) = - 0.7962

What is the general solution for cos(2x)*2-2cos(x)=0 ?
The general solution for cos(2x)*2-2cos(x)=0 is x=2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin