Find the principal and general solutions of the equation cosec x = – 2

Question

Find the principal and general solutions of the following equations: cosec x = – 2

Answer 1

cosec x = -2 

1/sinx = -2 

-2 sin x = 1 

sin x = -1/2 

x = arcsin (-1/2) = -π/6 ... principle solution 

x = π + π/6 ± 2nπ or x = 2π - π/6 ± 2nπ 

x = 7π/6 ± 2nπ or x = 11π/6 ± 2nπ ... general solution