What is the general solution for tan^5(x)+tan^3(x)=0 ?

The general solution for tan^5(x)+tan^3(x)=0 is x=pin

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tan^5(x)+tan^3(x)=0

tan^{5} (x) + tan^{3} (x) = 0

x = πn

Solution steps

tan^{5} (x) + tan^{3} (x) = 0

Solve by substitution

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

tan (x) = 0 : x = πn

tan (x) = i :

No Solution

tan (x) = - i :

No Solution

Combine all the solutions

x = πn

0 = cos (x) (1 - cos (x)) + sin^{2} (x)

sin (2 x) = 3 cos^{2} (x)

\frac{1}{cos ( x )} = 1.98

2 sin^{2} (3 θ) - 1 = 0

4 sin (4 θ - \frac{π}{3}) + 3 = 5

What is the general solution for tan^5(x)+tan^3(x)=0 ?
The general solution for tan^5(x)+tan^3(x)=0 is x=pin