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

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

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cos(2θ)=cos(3θ)

cos (2 θ) = cos (3 θ)

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

Solution steps

cos (2 θ) = cos (3 θ)

Subtract

cos (3 θ)

from both sides

cos (2 θ) - cos (3 θ) = 0

Rewrite using trig identities

2 sin (\frac{5 θ}{2}) sin (\frac{θ}{2}) = 0

Solving each part separately

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

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

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

Combine all the solutions

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

Merge Overlapping Intervals

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

θ, 2 sin (θ) = 1.5

cos (θ) = - 2109

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

sin (x) = 0.72555

15 = 10 sin (\frac{π}{20} (x + 10)) + 12

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