What is the general solution for 2cos^2(t)+3cos(t)=-1 ?

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

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2cos^2(t)+3cos(t)=-1

2 cos^{2} (t) + 3 cos (t) = - 1

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

Solution steps

2 cos^{2} (t) + 3 cos (t) = - 1

Solve by substitution

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

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

cos (t) = - 1 : t = π + 2 πn

Combine all the solutions

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

x, cos (x - y) = 1

x, cos (x - y) = 0

sin (a) + 1 = 2 1 - sin^{2} (a)

4 cos (x) - 3 = 0

cos (θ) cos (2 θ) + sin (θ) sin (2 θ) = \frac{1}{2}

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