Trigonometric EquationHard

Question

Which of the following is/are correct -

Options

A.(2014)^ln(cosecx)) < (2015) ^ln(cosecx)) ∀ x ∈

B. ∀ x ∈

C.(999)^ln(tanx) > (999)^ln(sinx) ∀ x ∈

D.(tan x)^{ln(sin x)} > (cot x)^{ln(sin x)} ∀ x ∈

Solution

∵ ∀ x ∈ , ln(cosec x) > 0
∀ x ∈ , ln(cos x) > 0
∀ x ∈ , ln(tan x) > ln sin x
∀ x ∈ , l n sin x < 0 & tan x < 1 < cotx.
Hence (A,B,C,D)

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