Question

$i \: need \: ya \: help$
Prove that: 1+sec theta-tan theta/1+sec theta+tan theta=1-sin theta/cos theta.​

Answer 1

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Answer 2

((1+secx-tanx)/(1+secx+tanx))×((1+secx-tanx)/(1+secx-tanx)). {As (1+secx-tanx)/(1+secx-tanx=1)}
(sec^2x+tan^2x+1+2secx-2tanx-2secx.tanx)/(1+sec^2x+ 2secx -tan^2x)
(2sec^2x+2+2secx-2 tanx-2secx.tanx)/(2 +2secx)
(As 1+tan^2x=sec^2x and sec^2x-tan^2x=1)

Factoize
2(secx-tanx)(secx+1)/2(secx+1)
=secx-tanx
1/cosx-sinx/cosx
=1-sinx/cosx