What is the general solution for 4cos^2(x)-3cos(x)-1=0 ?

The general solution for 4cos^2(x)-3cos(x)-1=0 is x=2pin,x=1.82347…+2pin,x=-1.82347…+2pin

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4cos^2(x)-3cos(x)-1=0

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

x = 2 πn, x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

Solution steps

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

Solve by substitution

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

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

x = 2 πn, x = arccos (- \frac{1}{4}) + 2 πn, x = - arccos (- \frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 2 πn, x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

2 sin^{2} (\frac{x}{3}) = 1

cos (2 x) = 3 - 5 sin (x)

4 cos^{2} (x) + 43 sin (x) = 7

cos (2 θ) - sin (θ) cos (θ) = 0

\frac{cos ( x )}{2} - \frac{1}{2} = 0

What is the general solution for 4cos^2(x)-3cos(x)-1=0 ?
The general solution for 4cos^2(x)-3cos(x)-1=0 is x=2pin,x=1.82347…+2pin,x=-1.82347…+2pin