Prove that 1+sec theta-tan theta/1+sec theta+tan theta=1-sin theta/cos theta
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Step-by-step explanation:
1+secA-tanA/1+secA+tanA
=1+secA-tanA/1+secA+tanA× secA+tanA/secA+tanA
=(secA+tanA)+sec²A-tan²A/(1+secA+tanA)(secA+tanA)
=secA+tanA+1/(1+secA+tanA) (secA+tanA)
=1/secA+tanA
=secA-tanA/sec²A-tan²A
=1/cosA-sinA/cosA
=1-sinA/cosA
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