In incrementABC,prove that :
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Asked by Olivia Adhikary | 4th Aug, 2014, 12:25: PM

Expert Answer:

L e t space a equals k space s i n space A comma space b equals k space s i n space B comma space c equals k space s i n space C left square bracket U s i n g space s i n e space r u l e right square bracket L H S comma k cubed s i n cubed A. s i n left parenthesis B minus C right parenthesis plus k cubed s i n cubed B. s i n left parenthesis C minus A right parenthesis plus k cubed s i n cubed C. s i n left parenthesis A minus B right parenthesis equals k cubed s i n squared A. s i n A. s i n left parenthesis B minus C right parenthesis plus k cubed s i n squared B. s i n B. s i n left parenthesis C minus A right parenthesis plus k cubed s i n squared C. s i n C. s i n left parenthesis A minus B right parenthesis equals k cubed sin squared A. sin left square bracket straight pi minus left parenthesis straight B plus straight C right parenthesis right square bracket. sin left parenthesis B minus C right parenthesis plus k cubed sin squared B. sin left square bracket straight pi minus left parenthesis straight C plus straight A right parenthesis right square bracket. sin left parenthesis C minus A right parenthesis plus k cubed sin squared C. sin left square bracket straight pi minus left parenthesis straight A plus straight B right parenthesis right square bracket. sin left parenthesis A minus B right parenthesis 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 left square bracket sin left parenthesis straight pi minus straight A right parenthesis equals sin space A right square bracket space equals k cubed sin squared A. sin left parenthesis straight B plus straight C right parenthesis. sin left parenthesis B minus C right parenthesis plus k cubed sin squared B. sin left parenthesis straight C plus straight A right parenthesis. sin left parenthesis C minus A right parenthesis plus k cubed sin squared C. sin left parenthesis A plus B right parenthesis. sin left parenthesis A minus B right parenthesis equals k cubed sin squared A. left parenthesis sin squared straight B minus sin squared C right parenthesis plus k cubed sin squared B. left parenthesis sin squared straight C minus sin squared A right parenthesis plus k cubed sin squared C. left parenthesis sin squared A minus sin squared B right parenthesis 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 space space space space space space space space space left square bracket sin left parenthesis A minus B right parenthesis. sin left parenthesis A plus B right parenthesis equals sin squared A minus sin squared B right square bracket equals k cubed sin squared A. sin squared straight B minus k cubed sin squared A. sin squared C plus k cubed sin squared B. sin squared straight C minus k cubed sin squared B. sin squared A plus k cubed sin squared C. sin squared A minus k cubed sin squared C. sin squared B equals 0 equals R H S H e n c e space P r o v e d

Answered by Prasenjit Paul | 5th Aug, 2014, 09:53: AM

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