Prove that 
begin mathsize 20px style open vertical bar table row cell sin squared A space space end cell cell sin A cos A space space space space end cell cell cos squared A end cell row cell sin squared B space space space end cell cell sin B cos B space space end cell cell cos squared B end cell row cell sin squared C space space space end cell cell sin C cos C space space end cell cell cos squared C end cell end table close vertical bar equals sin open parentheses A minus B close parentheses sin open parentheses B minus C close parentheses sin open parentheses C minus A close parentheses end style

Asked by sunil2791 | 22nd Jul, 2017, 09:26: AM

Expert Answer:

begin mathsize 16px style Mutiplying space and space dividing space by space 2 space then space multiply space 2 space to space column space 2.
1 half open vertical bar table row cell sin squared straight A end cell cell 2 sinAcosA end cell cell cos squared straight A end cell row cell sin squared straight B end cell cell 2 sinBcosB end cell cell cos squared straight B end cell row cell sin squared straight C end cell cell 2 sinCcosC end cell cell cos squared straight C end cell end table close vertical bar
1 half open vertical bar table row cell sin squared straight A end cell cell sin 2 straight A end cell cell cos squared straight A end cell row cell sin squared straight B end cell cell sin 2 straight B end cell cell cos squared straight B end cell row cell sin squared straight C end cell cell sin 2 straight C end cell cell cos squared straight C end cell end table close vertical bar
Use space straight R subscript 1 minus straight R subscript 2 space end subscript and space straight R subscript 2 space end subscript minus straight R subscript 3
sin squared straight A minus sin squared straight B
equals open parentheses sinA plus sinB close parentheses left parenthesis sinA minus sinB right parenthesis
equals open parentheses 2 sin fraction numerator straight A plus straight B over denominator 2 end fraction cos fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses open parentheses 2 cos fraction numerator straight A plus straight B over denominator 2 end fraction sin fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses
equals open parentheses 2 sin fraction numerator straight A plus straight B over denominator 2 end fraction cos fraction numerator straight A plus straight B over denominator 2 end fraction close parentheses open parentheses 2 sin fraction numerator straight A minus straight B over denominator 2 end fraction cos fraction numerator straight A minus straight B over denominator 2 end fraction close parentheses
equals sin left parenthesis straight A plus straight B right parenthesis sin left parenthesis straight A minus straight B right parenthesis
similarly space cos squared straight A minus cos squared straight B equals negative sin left parenthesis straight A plus straight B right parenthesis sin left parenthesis straight A minus straight B right parenthesis
do space it space for space second space row.
you space will space get space
1 half open vertical bar table row 0 cell 2 cos left parenthesis straight A plus straight B right parenthesis sin left parenthesis straight A minus straight B right parenthesis end cell cell negative sin left parenthesis straight A plus straight B right parenthesis sin left parenthesis straight A minus straight B right parenthesis end cell row 0 cell 2 cos left parenthesis straight B plus straight C right parenthesis sin left parenthesis straight B minus straight C right parenthesis end cell cell negative sin left parenthesis straight B plus straight C right parenthesis sin left parenthesis straight B minus straight C right parenthesis end cell row 1 cell sin 2 straight C end cell cell cos squared straight C end cell end table close vertical bar
Taking space common space sin left parenthesis straight A minus straight B right parenthesis space from space straight R subscript 1 space and space sin left parenthesis straight B minus straight C right parenthesis space from space straight R subscript 2
equals fraction numerator sin left parenthesis straight A minus straight B right parenthesis sin left parenthesis straight B minus straight C right parenthesis over denominator 2 end fraction open vertical bar table row 0 cell 2 cos left parenthesis straight A plus straight B right parenthesis end cell cell negative sin left parenthesis straight A plus straight B right parenthesis end cell row 0 cell 2 cos left parenthesis straight B plus straight C right parenthesis end cell cell negative sin left parenthesis straight B plus straight C right parenthesis end cell row 1 cell sin 2 straight C end cell cell cos squared straight C end cell end table close vertical bar
Try space to space solve space it space further. space If space you space will space have space doubt space please space send space us space the space snapshot
of space your space work. space We space will space guide space you.

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Answered by Sneha shidid | 24th Jul, 2017, 10:15: AM