What is the general solution for tan^2(x)-2tan(x)-5=0 ?

The general solution for tan^2(x)-2tan(x)-5=0 is x=1.28863…+pin,x=-0.96688…+pin

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tan^2(x)-2tan(x)-5=0

tan^{2} (x) - 2 tan (x) - 5 = 0

x = 1.28863 \dots + πn, x = - 0.96688 \dots + πn

Solution steps

tan^{2} (x) - 2 tan (x) - 5 = 0

Solve by substitution

tan (x) = 1 + 6, tan (x) = 1 - 6

tan (x) = 1 + 6 : x = arctan (1 + 6) + πn

tan (x) = 1 - 6 : x = arctan (1 - 6) + πn

Combine all the solutions

x = arctan (1 + 6) + πn, x = arctan (1 - 6) + πn

Show solutions in decimal form

x = 1.28863 \dots + πn, x = - 0.96688 \dots + πn

tan (x) = \frac{10}{11}

sin (θ) = \frac{9}{13}

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

cos (x) = 0, cos (x) = 0

sec^{2} (x) + 4 = 6

What is the general solution for tan^2(x)-2tan(x)-5=0 ?
The general solution for tan^2(x)-2tan(x)-5=0 is x=1.28863…+pin,x=-0.96688…+pin