What is the general solution for sin^3(x)+sin(x)=2sin^{22}(x) ?

The general solution for sin^3(x)+sin(x)=2sin^{22}(x) is x=2pin,x=pi+2pin,x= pi/2+2pin

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sin^3(x)+sin(x)=2sin^{22}(x)

sin^{3} (x) + sin (x) = 2 sin^{22} (x)

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

Solution steps

sin^{3} (x) + sin (x) = 2 sin^{22} (x)

Solve by substitution

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

\frac{1 + tan ^{2} ( x )}{1 + sec ( x )} = sec (x)

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

sin (5 x - 1) = \frac{4}{5}

sin^{2} (x) = \frac{1}{36}

tan (x) = 31

What is the general solution for sin^3(x)+sin(x)=2sin^{22}(x) ?
The general solution for sin^3(x)+sin(x)=2sin^{22}(x) is x=2pin,x=pi+2pin,x= pi/2+2pin