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Maths-

General

Easy

Question

In $straight capital delta A B C comma a squared cot invisible function application A plus b squared cot invisible function application B plus C squared cot invisible function application C equals$

$Δ$
$2 Δ$
$3 Δ$
$4 Δ$

Hint:

In this question we will use the area formula and then use some trigonometric formulas to equate and then use the same area formula at the end to get the required answer.

The correct answer is: $4 straight capital delta$

$increment equals fraction numerator a over denominator 2 sin space A end fraction equals fraction numerator b over denominator 2 space sin space b end fraction equals fraction numerator c over denominator 2 space sin space C end fraction a squared c o t space A plus b squared c o t space B plus c squared c o t space B equals left parenthesis 2 increment sin space A right parenthesis squared. c o t space A plus open parentheses 2 space increment sin space B close parentheses squared. c o t space B plus open parentheses 2 space increment sin space close parentheses squared. c o t space C equals 4 increment squared left parenthesis sin squared space A. c o t space A plus sin squared B. c o t space B plus sin squared C. c o t space C right parenthesis equals 2 increment squared left parenthesis 2 sin space A. cos space A plus 2 sin space B space. cos space B plus 2 sin space C. cos space C right parenthesis equals 2 increment squared left parenthesis sin space 2 A plus sin space 2 B plus sin space 2 C right parenthesis equals 2 increment squared left parenthesis 2 sin left parenthesis A plus B right parenthesis. cos left parenthesis A minus B right parenthesis plus 2. sin space C. cos space C right parenthesis equals 2 increment squared left parenthesis 2 sin left parenthesis straight pi minus straight c right parenthesis. cos left parenthesis A minus B right parenthesis plus 2. sin space C. cos space left parenthesis straight pi minus left parenthesis straight A plus straight B right parenthesis right parenthesis right parenthesis equals 4 increment squared sin space C left parenthesis cos left parenthesis A plus B right parenthesis plus cos left parenthesis A minus B right parenthesis right parenthesis equals 8 increment squared sin space A. sin space B. space sin space C equals 8 increment squared fraction numerator a over denominator 2 increment end fraction. fraction numerator b over denominator 2 increment end fraction. fraction numerator c over denominator 2 increment end fraction equals fraction numerator a b c over denominator increment end fraction$

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