What is the general solution for 8sin^3(x)=8sin(x) ?

The general solution for 8sin^3(x)=8sin(x) is x=2pin,x=pi+2pin,x=(3pi)/2+2pin,x= pi/2+2pin

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8sin^3(x)=8sin(x)

8 sin^{3} (x) = 8 sin (x)

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

Solution steps

8 sin^{3} (x) = 8 sin (x)

Solve by substitution

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

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

cos (θ) + 2 sec (θ) = - 3

3 tan^{2} (θ) + 7 tan (θ) - 2 = 4

4 sin^{2} (x) = 0

5 cos (2 θ) = - 5 cos (θ)

What is the general solution for 8sin^3(x)=8sin(x) ?
The general solution for 8sin^3(x)=8sin(x) is x=2pin,x=pi+2pin,x=(3pi)/2+2pin,x= pi/2+2pin