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

The general solution for cos^2(x)+3cos(x)=1 is x=1.26319…+2pin,x=2pi-1.26319…+2pin

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cos^2(x)+3cos(x)=1

cos^{2} (x) + 3 cos (x) = 1

x = 1.26319 \dots + 2 πn, x = 2 π - 1.26319 \dots + 2 πn

Solution steps

cos^{2} (x) + 3 cos (x) = 1

Solve by substitution

cos (x) = \frac{- 3 + 13}{2}, cos (x) = \frac{- 3 - 13}{2}

cos (x) = \frac{- 3 + 13}{2} : x = arccos (\frac{- 3 + 13}{2}) + 2 πn, x = 2 π - arccos (\frac{- 3 + 13}{2}) + 2 πn

cos (x) = \frac{- 3 - 13}{2} :

No Solution

Combine all the solutions

x = arccos (\frac{- 3 + 13}{2}) + 2 πn, x = 2 π - arccos (\frac{- 3 + 13}{2}) + 2 πn

Show solutions in decimal form

x = 1.26319 \dots + 2 πn, x = 2 π - 1.26319 \dots + 2 πn

cot^{2} (x) = \frac{tan ( x )}{2}

tan (θ) = \frac{3.2}{4.1}

5 sec (x) tan (x) = 0

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

6 arccos (4 x) = 5 π

What is the general solution for cos^2(x)+3cos(x)=1 ?
The general solution for cos^2(x)+3cos(x)=1 is x=1.26319…+2pin,x=2pi-1.26319…+2pin