What is the general solution for 5cos^2(x)-3cos(x)=2 ?

The general solution for 5cos^2(x)-3cos(x)=2 is x=2pin,x=1.98231…+2pin,x=-1.98231…+2pin

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

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

x = 2 πn, x = 1.98231 \dots + 2 πn, x = - 1.98231 \dots + 2 πn

Solution steps

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

Solve by substitution

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

cos (x) = 1 : x = 2 πn

cos (x) = - \frac{2}{5} : x = arccos (- \frac{2}{5}) + 2 πn, x = - arccos (- \frac{2}{5}) + 2 πn

Combine all the solutions

x = 2 πn, x = arccos (- \frac{2}{5}) + 2 πn, x = - arccos (- \frac{2}{5}) + 2 πn

Show solutions in decimal form

x = 2 πn, x = 1.98231 \dots + 2 πn, x = - 1.98231 \dots + 2 πn

9 tan^{2} (x) - 27 = 0

cos (x) = - 0.45

sin (4 x) cos (x) - sin (x) cos (4 x) = - \frac{1}{2}

4 tan (θ) - 1 = 0

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

What is the general solution for 5cos^2(x)-3cos(x)=2 ?
The general solution for 5cos^2(x)-3cos(x)=2 is x=2pin,x=1.98231…+2pin,x=-1.98231…+2pin