prove that cosA-sinA+1/cos A+sinA-1=cosecA+cotA
Answers
Question :--- prove that (cosA-sinA+1) / (cos A+sinA-1) = (cosecA+cotA)
Formula used :---
- CosA/sinA = cotA
- 1/sinA = cosA
- 1 = cosec²A - cot²A
- (a² - b²) = (a+b)(a-b)
Solution :---
→ (cos A- sin A + 1) / (cos A + sin A - 1).
Divide both numerator and the denominator by sinA we get ,,
→ (cosec A + cot A - 1)/(cotA - cosec A +1)
Now, Putting value of 1 = cosec²A - cot²A = (cosecA + cotA)(cosecA - cotA) in Numerator we get,
→ {(cosecA+cotA)-(cosecA+cotA)(cosecA-cotA)} / (cotA - cosec A +1)
Taking (cosecA+cotA) common From Numerator Now, we get,
→ [(cosecA+cotA){1-(cosecA-cotA)}] / (cotA - cosec A +1)
→ (cosecA+cotA)(cotA-cosecA+1) / (cotA - cosec A +1)
(cotA - cosec A +1) will be cancel now
So, we get,
==>>> (cosecA+cotA)
✪✪ Hence Proved ✪✪
Similar Question :---
Pls prove this question.
https://brainly.in/question/14417354?utm_source=android&utm_medium=share&utm_campaign=question
Answer:
nvnnnn
Step-by-step explanation:
that hggfttgjjkn h