What is the general solution for 2cos^2(x)-3cos(x)=2 ?

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

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2cos^2(x)-3cos(x)=2

2 cos^{2} (x) - 3 cos (x) = 2

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

Solution steps

2 cos^{2} (x) - 3 cos (x) = 2

Solve by substitution

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

cos (x) = 2 :

No Solution

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

Combine all the solutions

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

cot (θ) = \frac{1}{3}

- 3 sin^{2} (θ) + 4 sin (θ) - 7 = - 6

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

sin (x + \frac{π}{6}) + cos (x + \frac{π}{6}) = 1

sin (x) = - 1, 0 \leq x \leq 2 π

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