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

The general solution for sin^5(x)+sin^3(x)=0 is x=2pin,x=pi+2pin

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Solve by substitution

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = i :

No Solution

sin (x) = - i :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

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sin (a) + sin (12 0^{\circ} + a) + sin (12 0^{\circ} - a) = 0

3 sin (x) sin (x) = 5 cos (x) - 2

\frac{cos ( x ) + 3 cos ( x )}{2 + 2} = 0

What is the general solution for sin^5(x)+sin^3(x)=0 ?
The general solution for sin^5(x)+sin^3(x)=0 is x=2pin,x=pi+2pin