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

The general solution for 4cos^2(θ)-2=-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)-2=-1

4 cos^{2} (θ) - 2 = - 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) - 2 = - 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

sinh (x) = \frac{7}{24}, cosh (x)

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

sin (a) = \frac{15}{17}

cot (t) = 0

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

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