Question

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$\sf\color{red}{Prove\:That \: \sqrt{ \frac{1 + cos}{1 - cos} } = cosec + cot}$



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Answer 1

Step-by-step explanation:

I swear ! Making an answer 20 words long is hard

Answer 2

Step-by-step explanation:

(1 + cosA)/(1 - cosA) = cosecA + cotA

• Solving LHS

√[(1 + cosA)/(1 - cosA)]

• Rationalising LHS , we get

√[(1 + cosA)² / (1)² - (cosA)²]

• Using Identity a² - b² = (a+b)(a-b), we get

√[(1 + cosA)² / 1 - cos²A]

• 1 - cos²A = sin²A

√[(1 + cosA)² / sin²A]

(1 + cosA) / sinA

cosec A + cotA