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If `y=(log)_(sinx)(tanx),t h e n(((dy)/(dx)))_(pi/4)i se q u a lto` `4/(log2)` (b) `-4log2` `(-4)/(log2)` (d) none of these

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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