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

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

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

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

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

Solution steps

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

Solve by substitution

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

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

cos (t) = - 1 : t = π + 2 πn

Combine all the solutions

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

9 tan^{3} (x) = 3 tan (x)

cos (3 x) = 0.5, 0 < x < π

2 sin (3 x) = 1

cos (θ) - sin (θ) = 1

sin^{2} (x) - cos^{2} (x) + sin (x) = 0

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