Question

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

Answer 1

`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)"`