What is the general solution for 2cos^2(x)-5cos(x)-3=0 ?

The general solution for 2cos^2(x)-5cos(x)-3=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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2cos^2(x)-5cos(x)-3=0

2 cos^{2} (x) - 5 cos (x) - 3 = 0

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

Solution steps

2 cos^{2} (x) - 5 cos (x) - 3 = 0

Solve by substitution

cos (x) = 3, cos (x) = - \frac{1}{2}

cos (x) = 3 :

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 (x^{2}) = 0

cos (x) = - \frac{1}{4}

sin (\frac{x}{3}) = \frac{1}{2}

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

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

What is the general solution for 2cos^2(x)-5cos(x)-3=0 ?
The general solution for 2cos^2(x)-5cos(x)-3=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin