What is the general solution for 5cos^2(x)-6cos(x)+1=0 ?

The general solution for 5cos^2(x)-6cos(x)+1=0 is x=2pin,x=1.36943…+2pin,x=2pi-1.36943…+2pin

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5cos^2(x)-6cos(x)+1=0

5 cos^{2} (x) - 6 cos (x) + 1 = 0

x = 2 πn, x = 1.36943 \dots + 2 πn, x = 2 π - 1.36943 \dots + 2 πn

Solution steps

5 cos^{2} (x) - 6 cos (x) + 1 = 0

Solve by substitution

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

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

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

Show solutions in decimal form

x = 2 πn, x = 1.36943 \dots + 2 πn, x = 2 π - 1.36943 \dots + 2 πn

1 + sec^{2} (x) = tan^{2} (x)

cos (t) = \frac{1}{2}

3 cos^{2} (x) + 8 sin (x) = 7

csc (x + 1 0^{\circ}) = 3

6 tan (x) = 18 cot (x)

What is the general solution for 5cos^2(x)-6cos(x)+1=0 ?
The general solution for 5cos^2(x)-6cos(x)+1=0 is x=2pin,x=1.36943…+2pin,x=2pi-1.36943…+2pin