Prove the following trigonometric identities:
(secA-tanA)²=1-sinA/1+sinA
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(secA-tanA)² = Sec²A + Tan²A -2SecA.TanA proved
Step-by-step explanation:
(secA-tanA)² = Sec²A + Tan²A -2SecA.TanA
LHS (secA-tanA)² = 1/Cos²A + Sin²A/Cos²A - 2.1/Cos.SinA/CosA
= (1 + Sin²A - 2SinA) / Cos²A
= (1 -SinA)² / Cos²A
= (1 -SinA)² / (1 -Sin²A)
= (1 -SinA)(1 -SinA) / (1 -SinA)(1 +SinA)
= (1 -SinA) / (1 +SinA)
= RHS
LHS = RHS.
Hence proved.
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