Question

Find the principal value of the following: cosec^{- 1}(2)

Answer 1

The principal value branch of cosec^-1x  is `[- pi/2, pi/2] - {0}`.

Let cosec^-1(2) = α, `"where" (-pi)/(2) ≤ α ≤ pi/(2)`, α ≠ 0.

∴ cosec α = 2 = `"cosec"  pi/(6)`

∴ α = `pi/(6)                  ...[ ∵ - pi/2 ≤ pi/6 ≤ pi/2 ]`

∴ the principal value of cosec^-1(2) is `pi/(6)`.