prove : a CosA +bCos B+ c  COSC = 2a Sin B Sin C 

Asked by Kunmunsahoo.2012 | 25th Mar, 2015, 01:41: PM

Expert Answer:

W e space k n o w space t h a t space sin e space r u l e space i s colon fraction numerator a over denominator sin A end fraction equals fraction numerator b over denominator sin B end fraction equals fraction numerator c over denominator sin C end fraction equals R rightwards double arrow a equals R sin A semicolon space b equals R sin B semicolon c equals R sin C semicolon N o w space s u b s t i t u t i n g space t h e space v a l u e s space i n space L H S colon a cos A plus b cos B plus c cos C equals R sin A cos A plus R sin B cos B plus R sin C cos C equals R open square brackets sin A cos A plus sin B cos B plus sin C cos C close square brackets equals R over 2 open square brackets 2 sin A cos A plus 2 sin B cos B plus 2 sin C cos C close square brackets equals R over 2 open square brackets sin 2 A plus sin 2 B plus 2 sin C cos C close square brackets equals R over 2 open square brackets 2 sin open parentheses A plus B close parentheses cos open parentheses A minus B close parentheses plus 2 sin C cos C close square brackets equals R open square brackets sin open parentheses A plus B close parentheses cos open parentheses A minus B close parentheses plus sin C cos C close square brackets equals R open square brackets sin open parentheses straight pi minus straight C close parentheses cos open parentheses A minus B close parentheses plus sin C cos C close square brackets equals R open square brackets sin C cos open parentheses A minus B close parentheses plus sin C cos C close square brackets equals R sin C open square brackets cos open parentheses A minus B close parentheses plus cos C close square brackets equals R sin C open square brackets cos open parentheses A minus B close parentheses plus cos open parentheses straight pi minus open parentheses straight A plus straight B close parentheses close parentheses close square brackets equals R sin C open square brackets cos open parentheses A minus B close parentheses minus cos open parentheses straight A plus straight B close parentheses close square brackets equals R sin C open square brackets 2 sin A sin B close square brackets equals 2 open parentheses R sin A close parentheses sin B sin C equals 2 a sin B sin C space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets b y space sin e space r u l e close square brackets

Answered by Vimala Ramamurthy | 26th Mar, 2015, 09:48: AM

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