Trigonometric EquationMedium
Question
Which of the following is/are correct -
Options
A.(2014)ln(cosecx)) < (2015) ln(cosecx)) ∀ x ∈ 
B.
∀ x ∈
∀ 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)
, 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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