Solve for exact solutions csc(4x)=1 [0,2pi)

Answer 1

In general, csc(4x) takes the value 1 whenever 4x=(4n+1)π/2 and n is an integer, that is, whenever x=(4n+1)π/8. The only such values of x that also lie in the interval [0,2π) are π/8, 5π/8, 9π/8, and 13π/8.

Answer 2

csc 4x = 1

sin 4x = 1

4x = π/2

x = π/8