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

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

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

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

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

Solution steps

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

Switch sides

cos (2 x) + cos (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}

x, y = cos (4 x)

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

- 0.002 = sin (2 π \cdot (3) - 500 π (0) + x)

3 tan (2 x - \frac{π}{2}) = 2 sin (\frac{π}{3})

2 tan (x) - 2 = 0, 0 \leq x \leq 2 π

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