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

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

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

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

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

Solution steps

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

Switch sides

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}

8 cos^{2} (x) = 2

arctan (t) + 1 = 1

2 cos^{2} (θ) - 7 cos (θ) + 3 = 0, 0 < θ < 2 π

csc (θ) = \frac{3}{2}

12 cos^{2} (x) + 5 sin (x) - 9 = 0

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