solutions of physics
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We are required to find the derivative of (log tan x)Assume tan x to be y then the question becomes to find the derivative of log y.Hence, d/dx log (tan x) = 1/tan x . d/dx (tan x) ( using d/dx log x = 1/x) = 1/tan x . sec2 x. = (cos x)/ (sin x). 1/ cos2x = 1/ sin x cos xThis is the answer which if required can further be simplified as 2/ 2sin x cos xwhich becomes 2/ sin 2x = 2 cosec 2x.
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