What is the general solution for cos(5θ)-cos(7θ)=0 ?

The general solution for cos(5θ)-cos(7θ)=0 is θ=(pin)/3 ,θ= pi/6+(pin)/3 ,θ=2pin,θ=pi+2pin

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cos(5θ)-cos(7θ)=0

cos (5 θ) - cos (7 θ) = 0

θ = \frac{πn}{3}, θ = \frac{π}{6} + \frac{πn}{3}, θ = 2 πn, θ = π + 2 πn

Solution steps

cos (5 θ) - cos (7 θ) = 0

Rewrite using trig identities

2 sin (6 θ) sin (θ) = 0

Solving each part separately

sin (6 θ) = 0 or sin (θ) = 0

sin (6 θ) = 0 : θ = \frac{πn}{3}, θ = \frac{π}{6} + \frac{πn}{3}

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

Combine all the solutions

θ = \frac{πn}{3}, θ = \frac{π}{6} + \frac{πn}{3}, θ = 2 πn, θ = π + 2 πn

sin (x - \frac{π}{3}) = \frac{2}{2}

5 cos (a) + 4 = 0

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

sin (x) - 1 = - cos (2 x)

2 cos (\frac{x}{2}) - 2 = 0, 0 \leq x < 2 π

What is the general solution for cos(5θ)-cos(7θ)=0 ?
The general solution for cos(5θ)-cos(7θ)=0 is θ=(pin)/3 ,θ= pi/6+(pin)/3 ,θ=2pin,θ=pi+2pin