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

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

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

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

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

Solution steps

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

Solve by substitution

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

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

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

sin (θ) = - \frac{2}{5}

- sin^{2} (x) = 2 cos (x) - 2

3 sin (2 θ) - 5 sin (θ) = 0

cos (2 x) = cos (x), 0 \leq x \leq 2 π

tan (x) = \frac{3}{2}

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