What is the general solution for sin(x)+sin^2(x)+sin^3(x)=1 ?

The general solution for sin(x)+sin^2(x)+sin^3(x)=1 is x=0.57482…+2pin,x=pi-0.57482…+2pin

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sin(x)+sin^2(x)+sin^3(x)=1

sin (x) + sin^{2} (x) + sin^{3} (x) = 1

x = 0.57482 \dots + 2 πn, x = π - 0.57482 \dots + 2 πn

Solution steps

sin (x) + sin^{2} (x) + sin^{3} (x) = 1

Solve by substitution

sin (x) \approx 0.54368 \dots

sin (x) = 0.54368 \dots : x = arcsin (0.54368 \dots) + 2 πn, x = π - arcsin (0.54368 \dots) + 2 πn

Combine all the solutions

x = arcsin (0.54368 \dots) + 2 πn, x = π - arcsin (0.54368 \dots) + 2 πn

Show solutions in decimal form

x = 0.57482 \dots + 2 πn, x = π - 0.57482 \dots + 2 πn

\frac{cos ( a )}{1 + sin ( a )} = sec (a)

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

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

42 - 25 cos (x) = 31

2 sec^{2} (x) = 5 tan (x)

What is the general solution for sin(x)+sin^2(x)+sin^3(x)=1 ?
The general solution for sin(x)+sin^2(x)+sin^3(x)=1 is x=0.57482…+2pin,x=pi-0.57482…+2pin