What is the general solution for tan^2(x)-3tan(x)-4=0 ?

The general solution for tan^2(x)-3tan(x)-4=0 is x=1.32581…+pin,x=(3pi)/4+pin

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tan^2(x)-3tan(x)-4=0

tan^{2} (x) - 3 tan (x) - 4 = 0

x = 1.32581 \dots + πn, x = \frac{3 π}{4} + πn

Solution steps

tan^{2} (x) - 3 tan (x) - 4 = 0

Solve by substitution

tan (x) = 4, tan (x) = - 1

tan (x) = 4 : x = arctan (4) + πn

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

Combine all the solutions

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

Show solutions in decimal form

x = 1.32581 \dots + πn, x = \frac{3 π}{4} + πn

2 cos (x) + 4 = 5

cos (2 x - \frac{π}{2}) = - 1

cot (x) = - \frac{1}{3}

4 cos^{2} (x) + 2 cos (x) - 2 = 0

tan (3 x) = 0

What is the general solution for tan^2(x)-3tan(x)-4=0 ?
The general solution for tan^2(x)-3tan(x)-4=0 is x=1.32581…+pin,x=(3pi)/4+pin