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

The general solution for tan^2(x)-3tan(x)-2=0 is x=1.29706…+pin,x=-0.51166…+pin

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tan^2(x)-3tan(x)-2=0

tan^{2} (x) - 3 tan (x) - 2 = 0

x = 1.29706 \dots + πn, x = - 0.51166 \dots + πn

Solution steps

tan^{2} (x) - 3 tan (x) - 2 = 0

Solve by substitution

tan (x) = \frac{3 + 17}{2}, tan (x) = \frac{3 - 17}{2}

tan (x) = \frac{3 + 17}{2} : x = arctan (\frac{3 + 17}{2}) + πn

tan (x) = \frac{3 - 17}{2} : x = arctan (\frac{3 - 17}{2}) + πn

Combine all the solutions

x = arctan (\frac{3 + 17}{2}) + πn, x = arctan (\frac{3 - 17}{2}) + πn

Show solutions in decimal form

x = 1.29706 \dots + πn, x = - 0.51166 \dots + πn

sin (3 x) + 1 = cos (3 x)

6 sin^{2} (x) = 5

tan (θ) = \frac{46}{33}

arcsin (y) = \frac{1}{2}

500 = 2 cos (x)

What is the general solution for tan^2(x)-3tan(x)-2=0 ?
The general solution for tan^2(x)-3tan(x)-2=0 is x=1.29706…+pin,x=-0.51166…+pin