Prove the identity: `tanx/(secx+1) = (secx-1)/tanx`

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The identity `tan x/(sec x + 1) = (sec x - 1)/tan x` has to be proved.

`tan x/(sec x + 1)`

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

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

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

=> `((sin x)(1...

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The identity `tan x/(sec x + 1) = (sec x - 1)/tan x` has to be proved.

`tan x/(sec x + 1)`

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

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

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

=> `((sin x)(1 - cos x))/(1 - cos^2x)`

=> `((sin x)(1 - cos x))/(sin^2x)`

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

=> `(1/cos x - 1)/tan x`

=> `(sec x - 1)/tan x`

This proves that `tan x/(sec x + 1) = (sec x - 1)/tan x`

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