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

The general solution for cos^2(x)=3-5cos(x) is x=0.99871…+2pin,x=2pi-0.99871…+2pin

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

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

x = 0.99871 \dots + 2 πn, x = 2 π - 0.99871 \dots + 2 πn

Solution steps

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

Solve by substitution

cos (x) = \frac{- 5 + 37}{2}, cos (x) = \frac{- 5 - 37}{2}

cos (x) = \frac{- 5 + 37}{2} : x = arccos (\frac{- 5 + 37}{2}) + 2 πn, x = 2 π - arccos (\frac{- 5 + 37}{2}) + 2 πn

cos (x) = \frac{- 5 - 37}{2} :

No Solution

Combine all the solutions

x = arccos (\frac{- 5 + 37}{2}) + 2 πn, x = 2 π - arccos (\frac{- 5 + 37}{2}) + 2 πn

Show solutions in decimal form

x = 0.99871 \dots + 2 πn, x = 2 π - 0.99871 \dots + 2 πn

sin (x) = \frac{1}{sec ( x )}

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

1 = tan (\frac{x}{3})

cos (12 x) = 0

cos (2 x + 1) = \frac{1}{2}

What is the general solution for cos^2(x)=3-5cos(x) ?
The general solution for cos^2(x)=3-5cos(x) is x=0.99871…+2pin,x=2pi-0.99871…+2pin