Cos a /1+sin a=1-sin a/cosa
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Divide LHS by cosA,
tanA+secA−1/tanA−secA+1tanA+secA−1/tanA−secA+1
=tanA+secA−(sec2A−tan2A)/tanA−secA+1=tanA+secA−(sec2A−tan2A)/tanA−secA+1
=tanA+secA−[(tanA+secA)(secA−tanA)]/tanA−secA+1=tanA+secA−[(tanA+secA)(secA−tanA)]/tanA−secA+1
=(tanA+secA)1−secA+tanA/1−secA+tanA=(tanA+secA)1−secA+tanA/1−secA+tanA
=tanA+secA=tanA+secA
=(secA+tanA)(secA−tanA)/secA−tanA=(secA+tanA)(secA−tanA)/secA−tanA
=(sec2A−tan2A)/secA−tanA=(sec2A−tan2A)/secA−tanA
=1/secA−tanA=1/secA−tanA
R.H.S=L.H.SR.H.S=L.H.S
Hence proved
MARK BRAINLIEST..
tanA+secA−1/tanA−secA+1tanA+secA−1/tanA−secA+1
=tanA+secA−(sec2A−tan2A)/tanA−secA+1=tanA+secA−(sec2A−tan2A)/tanA−secA+1
=tanA+secA−[(tanA+secA)(secA−tanA)]/tanA−secA+1=tanA+secA−[(tanA+secA)(secA−tanA)]/tanA−secA+1
=(tanA+secA)1−secA+tanA/1−secA+tanA=(tanA+secA)1−secA+tanA/1−secA+tanA
=tanA+secA=tanA+secA
=(secA+tanA)(secA−tanA)/secA−tanA=(secA+tanA)(secA−tanA)/secA−tanA
=(sec2A−tan2A)/secA−tanA=(sec2A−tan2A)/secA−tanA
=1/secA−tanA=1/secA−tanA
R.H.S=L.H.SR.H.S=L.H.S
Hence proved
MARK BRAINLIEST..
aankit593:
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