The correct option (b) (2n + 1)(π/4), n ∈ z
Explanation:
tan(cot x) = cot(tan x)
∴ tan(cot x) = tan[(π/2) – tan x]
∴ cot x = nπ + (π/2) – tan x
∴ cot x + tan x = nπ + (π/2)
∴ [(cos x)/(sin x)] + [(sinx)/(cosx)] = (π/2)(2n + 1)
∴ [1/(sinx cosx)] = (π/2)(2n + 1)
∴ [2/(sin2x)] = (π/2)(2n + 1)
∴ 2cosec2x = (π/2)(2n + 1)
∴ cosec2x = (π/4)(2n + 1).