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

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

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

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

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

Solution steps

tan^{3} (x) - 1 \cdot tan (x) = 0

Solve by substitution

tan (x) = 0, tan (x) = - 1, tan (x) = 1

tan (x) = 0 : x = πn

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

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

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

2 cos (x) - 1 = 0, 0 \leq x \leq 2 π

tan (2 x) = 2

sin (2 x) = cos (2 x) + 1

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

y, sin (x) = x (1 + tan (y))

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