What is the general solution for 4sin(x)-sin^3(x)-1=0 ?

The general solution for 4sin(x)-sin^3(x)-1=0 is x=0.25691…+2pin,x=pi-0.25691…+2pin

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4sin(x)-sin^3(x)-1=0

4 sin (x) - sin^{3} (x) - 1 = 0

x = 0.25691 \dots + 2 πn, x = π - 0.25691 \dots + 2 πn

Solution steps

4 sin (x) - sin^{3} (x) - 1 = 0

Solve by substitution

sin (x) \approx 0.25410 \dots, sin (x) \approx 1.86080 \dots, sin (x) \approx - 2.11490 \dots

sin (x) = 0.25410 \dots : x = arcsin (0.25410 \dots) + 2 πn, x = π - arcsin (0.25410 \dots) + 2 πn

sin (x) = 1.86080 \dots :

No Solution

sin (x) = - 2.11490 \dots :

No Solution

Combine all the solutions

x = arcsin (0.25410 \dots) + 2 πn, x = π - arcsin (0.25410 \dots) + 2 πn

Show solutions in decimal form

x = 0.25691 \dots + 2 πn, x = π - 0.25691 \dots + 2 πn

1 - tan (a) = \frac{- 1}{3}

tan^{2} (x) + cos^{2} (x) - 1 = 0

cot^{3} (x) + cot (x) = 0

21 + 18 cos (x) = 16 (1 - cos^{2} (x))

sin (2 a + 10) = cos (3 a - 20)

What is the general solution for 4sin(x)-sin^3(x)-1=0 ?
The general solution for 4sin(x)-sin^3(x)-1=0 is x=0.25691…+2pin,x=pi-0.25691…+2pin