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

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Answer 1 · 2018-07-01T11:18:39

LHS= RHS (Verified)

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

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

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

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

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

$=sin x$ (Verified) [Ans]

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