What is the general solution for -5cos^2(x)+4cos(x)+1=0 ?

The general solution for -5cos^2(x)+4cos(x)+1=0 is x=1.77215…+2pin,x=-1.77215…+2pin,x=2pin

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-5cos^2(x)+4cos(x)+1=0

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

x = 1.77215 \dots + 2 πn, x = - 1.77215 \dots + 2 πn, x = 2 πn

Solution steps

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

Solve by substitution

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

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

cos (x) = 1 : x = 2 πn

Combine all the solutions

x = arccos (- \frac{1}{5}) + 2 πn, x = - arccos (- \frac{1}{5}) + 2 πn, x = 2 πn

Show solutions in decimal form

x = 1.77215 \dots + 2 πn, x = - 1.77215 \dots + 2 πn, x = 2 πn

sin (B) + cos (B) = 2

3 sin (x) + cos (2 x) = 2

cos (3 x) + cos (5 x) = cos (x)

sin (θ) + sin (θ) cos (θ) = 0

8 + 4 cos (2 x) = 12 cos (x)

What is the general solution for -5cos^2(x)+4cos(x)+1=0 ?
The general solution for -5cos^2(x)+4cos(x)+1=0 is x=1.77215…+2pin,x=-1.77215…+2pin,x=2pin