Question

Prove the following identity:

(1/tanx) + tanx = (1/sinx cosx)
I have attempted to convert 1 to sin^2x+cos^2x and then made both denominators equal but I am uncertain if I am correct or not. Thanks.

Answer 1

( 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.