Question

If y=logtanx, the find dx/dy

Answer 1

  Let p = tan x dp/dx = sec ² x y = log pdy/dp = 1 /p 
now,dy/dx = (1 / p) (sec ² x) 

⇒dy/dx = (1 / tan x) (sec ² x) 

⇒dy/dx = cot x sec ² x 

⇒dy/dx = (cos x / sin x) (1 / cos ² x) 

⇒dy/dx = 1 / ( sin x cos x)
 ⇒dy/dx = 2 / (2 sin x cos x) 

⇒dy/dx = 2 / sin 2x 

           or

dy/dx = 2 cosec 2x