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(*) If A+B = 225 degrees, then (cot A) / (1 + cot A ) . ( cot B) / (1 + cotB ) =

(*)
If A+B = 225 degrees, then (cot A) / (1 + cot A ) . ( cot B) / (1 + cotB ) =

Grade:11

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
Dear student

Please consider A. = 225, B = 0

Answer will be equal to 1

Regards
Vikas TU
14149 Points
4 years ago
Given A + B = 225 = B = 225 - A
= B = 180 + 45 - A = B = 180 + (45 - A) (As 225 = 180 + 45)
Putting value of B in question we get
cot A/(1 + cot A) * cot {180 + ( 45 - A)} / [ 1 + cot {180 + (45 - A)}
= cot A/(1 + cot A) * cot (45 - A) / [1 + cot (45 - A)] [As cot (180 + A) = cot A]
= cot A/(1 + cot A) * [ {cot 45cot A + 1 / cot A - cot 45} / {1 + (cot 45 cot A + 1) / (cot A - cot 45)}]
[As cot (A - B) = (cot B cot A + 1) / (cot B - cot A) ]
= cot A/(1 + cot A) * [ { cot A + 1 / cot A - 1} / {1 + ( cot A + 1) / (cot A - 1)}] (As cot 45 = 1)
= cot A/(1 + cot A) * [ { cot A + 1 / cot A - 1} / { (cot A - 1+ cot A + 1) / (cot A - 1)}] [ Taking L.C.M.]
= cot A/(1 + cot A) * [{cot A + 1 / cot A - 1} / { (2 cot A) / (cotA - 1)}]
= cot A/(1 + cot A) * (cot A + 1) / (cot A - 1) * (cot A - 1) / (2 cot A)
= 1/2

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