What is the general solution for cos^2(x)-3cos(x)-1=0 ?

The general solution for cos^2(x)-3cos(x)-1=0 is x=1.87839…+2pin,x=-1.87839…+2pin

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cos^2(x)-3cos(x)-1=0

cos^{2} (x) - 3 cos (x) - 1 = 0

x = 1.87839 \dots + 2 πn, x = - 1.87839 \dots + 2 πn

Solution steps

cos^{2} (x) - 3 cos (x) - 1 = 0

Solve by substitution

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

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

No Solution

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

Combine all the solutions

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

Show solutions in decimal form

x = 1.87839 \dots + 2 πn, x = - 1.87839 \dots + 2 πn

cos (3 x) = - sin (x + \frac{π}{6})

sin (θ) = \frac{7}{10}

tan (5 x) = 1

sec (5 x) = 2

5 sin (θ) - 1 = 3 sin (θ)

What is the general solution for cos^2(x)-3cos(x)-1=0 ?
The general solution for cos^2(x)-3cos(x)-1=0 is x=1.87839…+2pin,x=-1.87839…+2pin