What is the general solution for cos(3x)=cos(2x) ?

The general solution for cos(3x)=cos(2x) is x=(4pin)/5 ,x=(2pi)/5+(4pin)/5

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cos(3x)=cos(2x)

cos (3 x) = cos (2 x)

x = \frac{4 πn}{5}, x = \frac{2 π}{5} + \frac{4 πn}{5}

Solution steps

cos (3 x) = cos (2 x)

Subtract

cos (2 x)

from both sides

cos (3 x) - cos (2 x) = 0

Rewrite using trig identities

- 2 sin (\frac{5 x}{2}) sin (\frac{x}{2}) = 0

Solving each part separately

sin (\frac{5 x}{2}) = 0 or sin (\frac{x}{2}) = 0

sin (\frac{5 x}{2}) = 0 : x = \frac{4 πn}{5}, x = \frac{2 π}{5} + \frac{4 πn}{5}

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

Combine all the solutions

x = \frac{4 πn}{5}, x = \frac{2 π}{5} + \frac{4 πn}{5}, x = 4 πn, x = 2 π + 4 πn

Merge Overlapping Intervals

x = \frac{4 πn}{5}, x = \frac{2 π}{5} + \frac{4 πn}{5}

csc (x^{2}) = \frac{4}{3}

2 cos (x) cos^{3} (x) + cos^{2} (x) - sin^{2} (x) = cos (x)

tan (θ) = \frac{2 3}{- 2}

2 sin (2 x) = tan (2 x)

sin^{2} (3 a) = 0.56

What is the general solution for cos(3x)=cos(2x) ?
The general solution for cos(3x)=cos(2x) is x=(4pin)/5 ,x=(2pi)/5+(4pin)/5