What is the general solution for 10cos^2(x)+5cos(x)-5=0 ?

The general solution for 10cos^2(x)+5cos(x)-5=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

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10cos^2(x)+5cos(x)-5=0

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

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

Solution steps

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

Solve by substitution

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

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

2 sin (x) = - 3

3 sec (θ) - 2 = 0

4 cos (x) = 1

sin^{4} (x) = \frac{( cos ^{2} ( x ) )}{2}

cos^{2} (x) - cos (x) - 1 = 0

What is the general solution for 10cos^2(x)+5cos(x)-5=0 ?
The general solution for 10cos^2(x)+5cos(x)-5=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin