Question

How would you verify the identity `(secx-cosx+tanx)/(tanx+secx)=sinx`?

Answer 1

LHS= RHS (Verified)

Explanation:

`(sec x -cos x + tan x)/(tan x +sec x)`

`= (1/cos x -cos x + sin x/cos x)/(sin x/cos x +1/ cos x)`

`= ((1 -cos^2 x + sin x)/cancel cos x)/((sin x +1)/ cancelcos x)`

`= (sin ^2 x + sin x)/((sin x +1)`

`= (sin x cancel(( sin x +1)))/(cancel(sin x +1))`

`=sin x` (Verified) [Ans]