What is the general solution for -2cos^2(x)=3cos(x)+1 ?

The general solution for -2cos^2(x)=3cos(x)+1 is x=pi+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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-2cos^2(x)=3cos(x)+1

- 2 cos^{2} (x) = 3 cos (x) + 1

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

Solution steps

- 2 cos^{2} (x) = 3 cos (x) + 1

Solve by substitution

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

cos (x) = - 1 : x = π + 2 πn

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

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

1 + sec (x) = 3

tan (\frac{θ}{2} + \frac{π}{4}) = 1

cos^{2} (x) - 4 cos (x) + 3 = 0

sin^{2} (x) + 2 sin (x) + 1 = 0

4 cos^{2} (x) = 2

What is the general solution for -2cos^2(x)=3cos(x)+1 ?
The general solution for -2cos^2(x)=3cos(x)+1 is x=pi+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin