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

The general solution for 4cos^2(θ)=1 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

4 cos^{2} (θ) = 1

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

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 (x) = \frac{1}{2}

2 sin (x) = 2

cot (θ) = 1

sec^{2} (x) - 1 = 0

tan (θ) = \frac{3}{4}

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