( 1 / tan x ) + tan x = 1 / ( sin x cos x ) We will start with the left side: ( 1 / tan x ) + tan x = ( 1 / sinx/cosx ) + ( sin x / cos x ) = = ( cos x / sin x ) + ( sin x / cos x ) = = ( cos² x + sin² x ) / ( sin x cos x ) = = 1 / ( sin x cos x ) , which is same as the right side. The identity is proved.
