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0 votes
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in Mathematics by (75.1k points)

If tan(cot x) = cot(tanx) then cosec2x =

(a) (2n + 1)(π/2), n ∈ z

(b) (2n + 1)(π/4), n ∈ z

(c) [{n(n + 1)π}/2], n ∈ z

(d) (nπ/4), n ∈ z

1 Answer

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Best answer

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).

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