What is the general solution for 6cos^2(x)-5cos(x)=4 ?

The general solution for 6cos^2(x)-5cos(x)=4 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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6cos^2(x)-5cos(x)=4

6 cos^{2} (x) - 5 cos (x) = 4

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

Solution steps

6 cos^{2} (x) - 5 cos (x) = 4

Solve by substitution

cos (x) = \frac{4}{3}, cos (x) = - \frac{1}{2}

cos (x) = \frac{4}{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

cos (2 0^{\circ}) = sin (x)

2 cos (x) + sec (x) = 0

sec (2 x) = 1

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

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

What is the general solution for 6cos^2(x)-5cos(x)=4 ?
The general solution for 6cos^2(x)-5cos(x)=4 is x=(2pi)/3+2pin,x=(4pi)/3+2pin