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

  1.  straight capital delta
  2. 2 straight capital delta
  3. 3 straight capital delta
  4. 4 straight capital delta

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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