sin(B-C)/2 =b-c/a* cosA/2

Asked by nk.pandit02 | 15th Aug, 2016, 02:24: PM

Expert Answer:

begin mathsize 14px style L e t space fraction numerator a over denominator sin space A end fraction equals fraction numerator b over denominator sin B end fraction equals fraction numerator c over denominator sin C end fraction equals k
T h e n comma space a equals k sin A comma space b equals k sin B comma space c equals k sin C
R. H. S.
equals open parentheses fraction numerator b minus c over denominator a end fraction close parentheses cos A over 2
equals open parentheses fraction numerator k sin B minus k sin C over denominator k sin A end fraction close parentheses cos A over 2
equals open parentheses fraction numerator sin B minus sin C over denominator sin A end fraction close parentheses cos A over 2
equals fraction numerator 2 sin open parentheses begin display style fraction numerator B minus C over denominator 2 end fraction end style close parentheses cos open parentheses begin display style fraction numerator B plus C over denominator 2 end fraction end style close parentheses over denominator 2 sin begin display style A over 2 end style cos begin display style A over 2 end style end fraction cos A over 2
equals fraction numerator s i n open parentheses begin display style fraction numerator B minus C over denominator 2 end fraction end style close parentheses c o s open parentheses begin display style fraction numerator straight pi minus straight A over denominator 2 end fraction end style close parentheses over denominator s i n begin display style A over 2 end style end fraction
equals fraction numerator s i n open parentheses begin display style fraction numerator B minus C over denominator 2 end fraction end style close parentheses c o s open parentheses begin display style straight pi over 2 minus A over 2 end style close parentheses over denominator s i n begin display style A over 2 end style end fraction
equals fraction numerator s i n open parentheses begin display style fraction numerator B minus C over denominator 2 end fraction end style close parentheses sin open parentheses begin display style A over 2 end style close parentheses over denominator s i n begin display style A over 2 end style end fraction
equals s i n open parentheses fraction numerator B minus C over denominator 2 end fraction close parentheses
equals L. H. S. end style

Answered by Rashmi Khot | 16th Aug, 2016, 09:19: AM