What is the general solution for 6cos^2(x)-7cos(x)-5=0 ?

The general solution for 6cos^2(x)-7cos(x)-5=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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6cos^2(x)-7cos(x)-5=0

6 cos^{2} (x) - 7 cos (x) - 5 = 0

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

Solution steps

6 cos^{2} (x) - 7 cos (x) - 5 = 0

Solve by substitution

cos (x) = \frac{5}{3}, cos (x) = - \frac{1}{2}

cos (x) = \frac{5}{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 (x) = \frac{- 3}{5 sin ^{2} ( x )}

5 cos^{2} (x) - 12 sin^{2} (x) = 13

cos^{2} (x) - 0.5 cos (x) = 0

5 sin (x) cos (x) = 2 cos (x)

sin (x) = cos^{3} (x)

What is the general solution for 6cos^2(x)-7cos(x)-5=0 ?
The general solution for 6cos^2(x)-7cos(x)-5=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin