Which of the following is/are correct. (a) \( (\tan x)^{\ln (\sin x)}(\cot x)^{\ln (\sin x)}, \f...

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Which of the following is/are correct.
(a) \( (\tan x)^{\ln (\sin x)}(\cot x)^{\ln (\sin x)}, \forall x \in(0, \pi / 4) \)
(b) \( 4^{\ln \operatorname{cosec} x}5^{\ln \operatorname{cosec} x}, \forall x \in(0, \pi / 2) \)
(c) \( (1 / 2)^{\ln (\cos x)}(1 / 3)^{\ln (\cos x)}, \forall x \in(0, \pi / 2) \)
(d) \( 2^{\ln (\tan x)}2^{\ln (\tan x)}, \forall x \in(0, \pi / 2) \)
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