What is the general solution for 4cos^2(θ)-4cos(θ)-3=0 ?

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

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4cos^2(θ)-4cos(θ)-3=0

4 cos^{2} (θ) - 4 cos (θ) - 3 = 0

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

Solution steps

4 cos^{2} (θ) - 4 cos (θ) - 3 = 0

Solve by substitution

cos (θ) = \frac{3}{2}, cos (θ) = - \frac{1}{2}

cos (θ) = \frac{3}{2} :

No Solution

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

4 sin (x) + 3 cos (x) = 2

sec^{2} (x) + 7 tan (x) - 9 = 0

sin (x) = - 0.6

1 + sec^{2} (θ) = - 2

5 + 2 sin^{2} (x) = 3 sin (x) + 4

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