What is the general solution for cos(2x)+cos(x)=0,(0,2pi) ?

The general solution for cos(2x)+cos(x)=0,(0,2pi) is x= pi/3 ,x=pi,x=(5pi)/3

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cos(2x)+cos(x)=0,(0,2pi)

cos (2 x) + cos (x) = 0, (0, 2 π)

x = \frac{π}{3}, x = π, x = \frac{5 π}{3}

Solution steps

cos (2 x) + cos (x) = 0, (0, 2 π)

Rewrite using trig identities

2 cos (\frac{3 x}{2}) cos (\frac{x}{2}) = 0

Solving each part separately

cos (\frac{3 x}{2}) = 0 or cos (\frac{x}{2}) = 0

cos (\frac{3 x}{2}) = 0, (0, 2 π) : x = \frac{π}{3}, x = π, x = \frac{5 π}{3}

cos (\frac{x}{2}) = 0, (0, 2 π) : x = π

Combine all the solutions

x = \frac{π}{3}, x = π, x = \frac{5 π}{3}

cos (3 θ) = 1, 0 \leq θ \leq 2 π

3 \cdot sin (\frac{x}{2}) + cos (x) = 1

sin (2 x) = \frac{2}{3}

tan^{3} (θ) + tan^{2} (θ) - 3 tan (θ) - 3 = 0

x, sec (x) tan (x) = 0

What is the general solution for cos(2x)+cos(x)=0,(0,2pi) ?
The general solution for cos(2x)+cos(x)=0,(0,2pi) is x= pi/3 ,x=pi,x=(5pi)/3