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if y=log(sinx) tanx then ((dy)/(dx)) (pi...

if `y=log_(sinx) tanx` then `((dy)/(dx)) _(pi/4)` is

A

`(4)/(log 2)`

B

`-4 log 2`

C

`(-4)/( log 2)`

D

none of these

Text Solution

Verified by Experts

`y=(log tan x)/(log sin x)`
`therefore" "(dy)/(dx)=((log sin x)((sec^(2)x)/(tan x))-(log tan x )(cot x))/((log sin x)^(3))`
`"or "((dy)/(dx))_(pi//4)=(-4)/(log 2)" (On simplification)"`
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