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

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

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

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

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

Solution steps

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

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

cos (\frac{x}{2}) = 0 : x = π + 4 πn, x = 3 π + 4 πn

Combine all the solutions

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

Merge Overlapping Intervals

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

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

2 cos (x) + 2 = 0

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

2 sin (x) + 2 = 0

sin (2 x) = 2 sin (x)

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