What is the general solution for 2cos^2(x)-9cos(x)-5=0 ?

The general solution for 2cos^2(x)-9cos(x)-5=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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2cos^2(x)-9cos(x)-5=0

2 cos^{2} (x) - 9 cos (x) - 5 = 0

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

Solution steps

2 cos^{2} (x) - 9 cos (x) - 5 = 0

Solve by substitution

cos (x) = 5, cos (x) = - \frac{1}{2}

cos (x) = 5 :

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

2 sec^{2} (x) = 3 - tan (x)

2 sin^{2} (θ) - sin (θ) = 1

2 sin (- 3 x - \frac{π}{4}) = 2

4 sin^{3} (θ) - 3 sin (θ) = 0

\frac{sec ^{2} ( θ ) - 1}{1 - cos ^{2} ( θ )} - 1 = cot^{2} (θ)

What is the general solution for 2cos^2(x)-9cos(x)-5=0 ?
The general solution for 2cos^2(x)-9cos(x)-5=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin