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

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

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2(1-cos^2(x))-cos(x)-1=0

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

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

Solution steps

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

Solve by substitution

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

cos (x) = - 1 : x = π + 2 πn

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

Combine all the solutions

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

- sin (2 x) (2) = 0

cos (5 x - 21) = sin (13 - 3 x)

sin (θ) = \frac{5}{3}

cos (2 θ) + 14 sin^{2} (θ) = 10, 0 < θ < 2 π

14 sin^{2} (x) + 5 sin (x) - 1 = 0

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