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

The general solution for 3tan^3(x)+3tan^2(x)-tan(x)-1=0 is x=(3pi)/4+pin,x=(5pi)/6+pin,x= pi/6+pin

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

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

x = \frac{3 π}{4} + πn, x = \frac{5 π}{6} + πn, x = \frac{π}{6} + πn

Solution steps

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

Solve by substitution

tan (x) = - 1, tan (x) = - \frac{3}{3}, tan (x) = \frac{3}{3}

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

tan (x) = - \frac{3}{3} : x = \frac{5 π}{6} + πn

tan (x) = \frac{3}{3} : x = \frac{π}{6} + πn

Combine all the solutions

x = \frac{3 π}{4} + πn, x = \frac{5 π}{6} + πn, x = \frac{π}{6} + πn

8 sin (x) = 4 cos^{2} (x) - 7

cos (x) - 1 = 0, 0 \leq x \leq 2 π

sin (x) = \frac{4.8}{5.5}

2 cos^{2} (x) = 4 - 5 sin (x)

2 csc (2 x) + 2 = 0

What is the general solution for 3tan^3(x)+3tan^2(x)-tan(x)-1=0 ?
The general solution for 3tan^3(x)+3tan^2(x)-tan(x)-1=0 is x=(3pi)/4+pin,x=(5pi)/6+pin,x= pi/6+pin