What is the general solution for -4cos^2(θ)+1=0 ?

The general solution for -4cos^2(θ)+1=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ=(2pi)/3+2pin,θ=(4pi)/3+2pin

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-4cos^2(θ)+1=0

- 4 cos^{2} (θ) + 1 = 0

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn, θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

Solution steps

- 4 cos^{2} (θ) + 1 = 0

Solve by substitution

cos (θ) = \frac{1}{2}, cos (θ) = - \frac{1}{2}

cos (θ) = \frac{1}{2} : θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

cos (θ) = - \frac{1}{2} : θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

Combine all the solutions

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn, θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

sin (2 x) - sin (4 x) + sin (6 x) = 0

2 csc (x) - 3 = 0

cos (θ) = \frac{8}{12}

sin (x) sin (2 x) = 0

sin (x) = 1.2

What is the general solution for -4cos^2(θ)+1=0 ?
The general solution for -4cos^2(θ)+1=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ=(2pi)/3+2pin,θ=(4pi)/3+2pin