Question

prove that cosA-sinA+1/cos A+sinA-1=cosecA+cotA​

Answer 1

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 ✪✪

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Answer 2

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Step-by-step explanation:

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