What is the general solution for cos(3x)-cos(2x)=0 ?

The general solution for cos(3x)-cos(2x)=0 is x=(4pin)/5 ,x=(2pi)/5+(4pin)/5

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

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

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

Solution steps

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}

tan (2 x + 1 0^{\circ}) = 1.5

- 5 sec^{2} (x) - 10 sec (x) = - 15

tan (x + 2 0^{\circ}) = cot (x)

2 sin (θ) = cot (θ)

3 csc^{2} (x) + 1 = 5

What is the general solution for cos(3x)-cos(2x)=0 ?
The general solution for cos(3x)-cos(2x)=0 is x=(4pin)/5 ,x=(2pi)/5+(4pin)/5