If tan B = 2sinA sinC/ sin (A+C) , show that cotA,cotBand cotC are in A.P .

Asked by Sanjay | 13th May, 2015, 12:20: AM

Expert Answer:

tan space B equals fraction numerator 2 sin space A. sin space C over denominator sin space left parenthesis A plus C right parenthesis end fraction rightwards double arrow c o t space B equals fraction numerator sin space left parenthesis A plus C right parenthesis over denominator 2 space sin space A. sin space C end fraction rightwards double arrow c o t space B equals fraction numerator sin space A. cos space C plus sin space C. cos space A over denominator 2 space sin space A. sin space C end fraction rightwards double arrow 2 c o t space B equals fraction numerator sin space A. cos space C over denominator space sin space A. sin space C end fraction plus fraction numerator sin space C. cos space A over denominator sin space A. sin space C end fraction rightwards double arrow 2 space c o t space B equals c o t space C plus c o t space A therefore c o t space B equals fraction numerator c o t space A plus c o t space C over denominator 2 end fraction therefore c o t space A comma space c o t space B space a n d space c o t space C thin space a r e space i n space A P.

Answered by Prasenjit Paul | 13th May, 2015, 10:33: AM

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