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

The general solution for tan^3(x)+tan^2(x)-tan(x)-1=0 is x=(3pi)/4+pin,x= pi/4+pin

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tan^3(x)+tan^2(x)-tan(x)-1=0

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

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

Solution steps

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

Solve by substitution

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

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

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

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

tan (θ) = \frac{- 4 3}{4}

3 sin (x) - cos (x) = 3, 0 \leq x \leq 2 π

- 1 + 3 sin (x) = - 1 + 4 sin (x)

cos (x) = \frac{6}{25}

3 sin (φ) - cos (2 φ) = 1

What is the general solution for tan^3(x)+tan^2(x)-tan(x)-1=0 ?
The general solution for tan^3(x)+tan^2(x)-tan(x)-1=0 is x=(3pi)/4+pin,x= pi/4+pin