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

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

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sin^5(x)-sin(x)=0

sin^{5} (x) - sin (x) = 0

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

Solution steps

sin^{5} (x) - sin (x) = 0

Solve by substitution

sin (x) = 0, sin (x) = i, sin (x) = - i, sin (x) = - 1, sin (x) = 1

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = i :

No Solution

sin (x) = - i :

No Solution

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

tan (x) = \frac{95.75}{4}

5 cos^{2} (x) = 4

cos (x - 1 5^{0}) = \frac{( 2 )}{2}

sin (x) = 1 - cos^{x} (x)

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

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