What is the general solution for cos^2(x)-9cos(x)-1=0 ?

The general solution for cos^2(x)-9cos(x)-1=0 is x=1.68079…+2pin,x=-1.68079…+2pin

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cos^2(x)-9cos(x)-1=0

cos^{2} (x) - 9 cos (x) - 1 = 0

x = 1.68079 \dots + 2 πn, x = - 1.68079 \dots + 2 πn

Solution steps

cos^{2} (x) - 9 cos (x) - 1 = 0

Solve by substitution

cos (x) = \frac{9 + 85}{2}, cos (x) = \frac{9 - 85}{2}

cos (x) = \frac{9 + 85}{2} :

No Solution

cos (x) = \frac{9 - 85}{2} : x = arccos (\frac{9 - 85}{2}) + 2 πn, x = - arccos (\frac{9 - 85}{2}) + 2 πn

Combine all the solutions

x = arccos (\frac{9 - 85}{2}) + 2 πn, x = - arccos (\frac{9 - 85}{2}) + 2 πn

Show solutions in decimal form

x = 1.68079 \dots + 2 πn, x = - 1.68079 \dots + 2 πn

3 tan (x) = 2 sin (x)

12 arcsin (x) = 4 π

sec (x) = 2, 0 \leq x \leq 2 π

cos (2 x) + cos (3 x) = 0

cos (θ) = - 0.73

What is the general solution for cos^2(x)-9cos(x)-1=0 ?
The general solution for cos^2(x)-9cos(x)-1=0 is x=1.68079…+2pin,x=-1.68079…+2pin