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

The general solution for sin(x)n=3 is x=arcsin(3/n)+2pik,x=pi+arcsin(-3/n)+2pik

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sin(x)n=3

sin (x) n = 3

x = arcsin (\frac{3}{n}) + 2 πk, x = π + arcsin (- \frac{3}{n}) + 2 πk

Solution steps

sin (x) n = 3

Divide both sides by

n; n \neq = 0

sin (x) = \frac{3}{n}; n \neq = 0

Apply trig inverse properties

x = arcsin (\frac{3}{n}) + 2 πk, x = π + arcsin (- \frac{3}{n}) + 2 πk

3 cos (2 x) = 4 - 11 cos (x)

x, 2 cos^{2} (x) - cos (x) = 0

8 tan (2 x) - 5 = 3

- 8 cos (x) = 3

tan (x) \cdot cos (x) + cos (x) = 0

What is the general solution for sin(x)n=3 ?
The general solution for sin(x)n=3 is x=arcsin(3/n)+2pik,x=pi+arcsin(-3/n)+2pik