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Asked by veenitkumar4 | 12 Apr, 2019, 11:33: PM
answered-by-expert Expert Answer
G i v e n colon space A plus B plus C plus D equals 180 degree T O space p r o v e colon space sin A space sin B space plus space sin C space sin D equals space sin left parenthesis B plus C right parenthesis times sin left parenthesis B plus D right parenthesis C o n s i d e r comma space L H S equals space sin A space sin B space plus space sin C space sin D equals fraction numerator cos left parenthesis A minus B right parenthesis minus cos left parenthesis A plus B right parenthesis over denominator 2 end fraction plus fraction numerator cos left parenthesis C minus D right parenthesis minus cos left parenthesis C plus D right parenthesis over denominator 2 end fraction equals fraction numerator cos left parenthesis A minus B right parenthesis minus cos left parenthesis A plus B right parenthesis plus cos left parenthesis C minus D right parenthesis minus cos left parenthesis C plus D right parenthesis over denominator 2 end fraction equals fraction numerator cos left parenthesis A minus B right parenthesis plus cos left parenthesis C plus D right parenthesis plus cos left parenthesis C minus D right parenthesis minus cos left parenthesis C plus D right parenthesis over denominator 2 end fraction space.... space S i n c e space A plus B equals 180 degree minus left parenthesis C plus D right parenthesis space a n d space cos left parenthesis straight pi minus straight x right parenthesis equals negative cos x equals fraction numerator cos left parenthesis A minus B right parenthesis plus cos left parenthesis C minus D right parenthesis over denominator 2 end fraction space equals fraction numerator 2 cos open parentheses begin display style fraction numerator A minus B plus C minus D over denominator 2 end fraction end style close parentheses plus cos open parentheses begin display style fraction numerator A minus B minus left parenthesis C minus D right parenthesis over denominator 2 end fraction end style close parentheses over denominator 2 end fraction space equals cos open parentheses fraction numerator A minus B plus C minus D over denominator 2 end fraction close parentheses plus cos open parentheses fraction numerator A minus B minus C plus D right parenthesis over denominator 2 end fraction close parentheses space equals cos open parentheses fraction numerator A plus C minus left parenthesis B plus D right parenthesis over denominator 2 end fraction close parentheses plus cos open parentheses fraction numerator A plus D minus left parenthesis B plus C right parenthesis over denominator 2 end fraction close parentheses equals cos open parentheses fraction numerator 180 degree minus left parenthesis B plus D right parenthesis minus left parenthesis B plus D right parenthesis over denominator 2 end fraction close parentheses plus cos open parentheses fraction numerator 180 degree minus left parenthesis B plus C right parenthesis minus left parenthesis B plus C right parenthesis over denominator 2 end fraction close parentheses space space equals cos open parentheses 90 degree minus left parenthesis B plus D right parenthesis close parentheses plus cos open parentheses 90 degree minus left parenthesis B plus C right parenthesis close parentheses space space equals sin left parenthesis B plus D right parenthesis sin left parenthesis B plus C right parenthesis space......... space S i n c e space cos left parenthesis 90 degree minus x right parenthesis equals sin x H e n c e comma space sin A space sin B space plus space sin C space sin D equals space sin left parenthesis B plus C right parenthesis times sin left parenthesis B plus D right parenthesis
Answered by Renu Varma | 15 Apr, 2019, 02:27: PM

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