Maths-
General
Easy

Question

text  In  end text straight triangle A B C comma straight capital sigma fraction numerator a squared sin invisible function application left parenthesis B minus C right parenthesis over denominator sin invisible function application A end fraction equals

  1. a squared b squared
  2. b squared c squared
  3. c squared a squared
  4. 0

Hint:

In this question we will simplify the sequence first using sine formula and at the last we will get the required value.

The correct answer is: 0


    text  In  end text straight triangle A B C comma straight capital sigma fraction numerator a squared sin degree left parenthesis B minus C right parenthesis over denominator sin degree A end fraction equals fraction numerator straight a squared sin degree left parenthesis straight B minus straight C right parenthesis over denominator sin degree straight A end fraction plus fraction numerator straight b squared sin degree left parenthesis straight C minus straight A right parenthesis over denominator sin degree straight B end fraction plus fraction numerator straight c squared sin degree left parenthesis straight A minus straight B right parenthesis over denominator sin degree straight C end fraction
using space sine space formula comma
fraction numerator straight a over denominator sin space straight A end fraction equals fraction numerator straight b over denominator sin space straight B end fraction equals fraction numerator straight c over denominator sin space straight C end fraction equals straight k
fraction numerator straight a squared sin degree left parenthesis straight B minus straight C right parenthesis over denominator sin degree straight A end fraction plus fraction numerator straight b squared sin degree left parenthesis straight C minus straight A right parenthesis over denominator sin degree straight B end fraction plus fraction numerator straight c squared sin degree left parenthesis straight A minus straight B right parenthesis over denominator sin degree straight C end fraction
equals fraction numerator straight k squared sin squared straight A open parentheses sin open parentheses straight B minus straight C close parentheses close parentheses over denominator sinA end fraction plus fraction numerator straight k squared sin squared straight B open parentheses sin open parentheses straight C minus straight A close parentheses close parentheses over denominator sin space straight B end fraction plus fraction numerator straight k squared sin squared straight C open parentheses sin open parentheses straight A minus straight B close parentheses close parentheses over denominator sinC end fraction
equals straight k squared open square brackets sin space straight A space sin open parentheses straight B minus straight C close parentheses plus sinB left parenthesis sin open parentheses straight C minus straight A close parentheses plus sinC open parentheses sin open parentheses straight A minus straight B close parentheses close parentheses close square brackets
equals straight k squared open square brackets sin open parentheses straight pi minus open parentheses straight B plus straight C close parentheses close parentheses space sin open parentheses straight B minus straight C close parentheses plus sin open parentheses straight pi minus open parentheses straight C plus straight A close parentheses close parentheses left parenthesis sin open parentheses straight C minus straight A close parentheses plus sin open parentheses straight pi minus open parentheses straight A plus straight B close parentheses close parentheses open parentheses sin open parentheses straight A minus straight B close parentheses close parentheses close square brackets
equals straight k squared open square brackets sin left parenthesis straight B plus straight C right parenthesis space sin open parentheses straight B minus straight C close parentheses plus sin left parenthesis straight C plus straight A right parenthesis left parenthesis sin open parentheses straight C minus straight A close parentheses plus sin left parenthesis straight A plus straight B right parenthesis open parentheses sin open parentheses straight A minus straight B close parentheses close parentheses close square brackets
equals straight k squared open square brackets sin squared straight B minus sin squared straight C plus sin squared straight C minus sin squared straight A plus sin squared straight A minus sin squared straight B close square brackets
equals straight k squared cross times 0
equals 0.

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