simA-cosA+1/sinA+cosA-1=1/secA×tanA. prove
Answers
Correct Question: (sinA - cosA + 1)/(sinA + cosA - 1) = 1/(secA - tanA)
Explanation
1. Multiply L.H.S by (sinA + cosA + 1)/(sinA + cosA + 1). Apply all algebraic formulas.
2. Use Trignometric identities and take common terms out.
3. Solve R.H.S and bring out same fraction as in L.H.S we get on solving.
4. Hence Proved
Correct Question :-- Prove that (sin A-cos A+1)/(sin A+cosA-1)=1/(sec A-tan A)
Formula used :---
- 1 = sec²A - tan²A = (secA + TanA)
- SinA/cosA = TanA
- 1/CosA = SecA
Solution :---
Dividing the L.H.S. Numerator and denominator by cos A we get,
→ (tan A-1+secA)/(tan A+1-sec A)
→ (tan A-1+secA)/(1-sec A+tan A)
Now , Putting 1 = (sec A+tan A)(secA-tanA) in Denominator , we get,
→(sec A+tan A-1)/[(sec A+tan A)(sec A-tan A)-(sec A-tan A)]
Taking (secA-tanA) common From Denominator now ,
→ (sec A+tan A-1)/(sec A-tan A)(sec A+tan A-1)