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

The general solution for tan^2(x)-2tan(x)-3=0 is x=1.24904…+pin,x=(3pi)/4+pin

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

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

x = 1.24904 \dots + πn, x = \frac{3 π}{4} + πn

Solution steps

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

Solve by substitution

tan (x) = 3, tan (x) = - 1

tan (x) = 3 : x = arctan (3) + πn

tan (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = arctan (3) + πn, x = \frac{3 π}{4} + πn

Show solutions in decimal form

x = 1.24904 \dots + πn, x = \frac{3 π}{4} + πn

6 cos (x) - 3 = 0

cos^{2} (x) - 1 = 0, 0 \leq x \leq 2 π

2 tan^{2} (x) - tan (x) - 6 = 0

15 cos (x) + 8 = - cos (x)

cos (2 x + \frac{π}{6}) = \frac{3}{2}

What is the general solution for tan^2(x)-2tan(x)-3=0 ?
The general solution for tan^2(x)-2tan(x)-3=0 is x=1.24904…+pin,x=(3pi)/4+pin