25.Prove that
Sin A-Cos A+1/Sin A+ Cos A-1
=1/Sec A-Tan A
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Answer:
Step-by-step explanation:
Sin A-Cos A+1/Sin A+ Cos A-1
//multiply numerator and denominator by Sin A+ Cos A +1
=> (Sin A- Cos A + 1)(Sin A+ Cos A + 1) / (Sin A+ Cos A - 1)(Sin A+ Cos A +1)
=> [(SinA+1)² - Cos²A] / [(SinA+CosA)² - 1]
=> [Sin²A + 1 + 2SinA - Cos²A] / [Sin²A + Cos²A + 2SinACosA - 1]
=> [2Sin²A + 2SinA] / 2SinAcosA
=> 2SinA(SinA + 1) / 2SinACosA
=> SinA + 1 /CosA
=> SinA/CosA + 1/CosA
=> TanA + SecA
//Multiply and divide by SecA - TanA
=> (SecA - TanA)(SecA + TanA) / SecA - TanA
=> Sec²A - Tan²A / SecA - TanA
=> 1/SecA - TanA
=> R.H.S
Hence proved.
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