What is the general solution for 2cos^2(x)-3cos(x)-2=0 ?

The general solution for 2cos^2(x)-3cos(x)-2=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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2cos^2(x)-3cos(x)-2=0

2 cos^{2} (x) - 3 cos (x) - 2 = 0

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

Solution steps

2 cos^{2} (x) - 3 cos (x) - 2 = 0

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

sin (2 x) csc (2 x) - 2 sin (2 x) = 0

2 sin^{3} (x) + sin^{2} (x) - 2 sin (x) - 1 = 0

5 cos^{2} (θ) + cos (θ) = 0

x, z = sin (x y)

3 sec (x) + 3 tan (x) = 3

What is the general solution for 2cos^2(x)-3cos(x)-2=0 ?
The general solution for 2cos^2(x)-3cos(x)-2=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin