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प्रश्न
Find the principal value of the following: cosec- 1(2)
उत्तर
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)`.
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