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

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

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

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

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

Solution steps

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

Rewrite using trig identities

- 2 sin (\frac{3 x}{2}) sin (\frac{x}{2}) = 0

Solving each part separately

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

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

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

Combine all the solutions

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

Merge Overlapping Intervals

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

sin (4 x) + 1 = 0

4 cos^{2} (θ) = 3

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

tan (x) - 3 cot (x) = 0

sin (\frac{θ}{2}) = - \frac{1}{2}

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