What is the general solution for -3cos^2(x)+2cos(x)+1=0 ?

The general solution for -3cos^2(x)+2cos(x)+1=0 is x=1.91063…+2pin,x=-1.91063…+2pin,x=2pin

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-3cos^2(x)+2cos(x)+1=0

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

x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn, x = 2 πn

Solution steps

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

Solve by substitution

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

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

cos (x) = 1 : x = 2 πn

Combine all the solutions

x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn, x = 2 πn

Show solutions in decimal form

x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn, x = 2 πn

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

cos (x + \frac{3 π}{2}) + 2 sin (x + π) = 0

3 + 6 sin (3 x) = 0

cos (x) cos (2 x) - sin (x) sin (2 x) = 0

θ, x = 5 tan (θ)

What is the general solution for -3cos^2(x)+2cos(x)+1=0 ?
The general solution for -3cos^2(x)+2cos(x)+1=0 is x=1.91063…+2pin,x=-1.91063…+2pin,x=2pin