ELIMINATE A and B if , tanA + tanB = b , cotA + cotB = a and A+B = C .

Asked by Sanjay | 13th May, 2015, 11:35: AM

Expert Answer:

tan A plus tan B equals b... left parenthesis 1 right parenthesis c o t A plus c o t B equals a... left parenthesis 2 right parenthesis rightwards double arrow fraction numerator 1 over denominator tan A end fraction plus fraction numerator 1 over denominator tan B end fraction equals a rightwards double arrow fraction numerator tan A plus tan B over denominator tan A. tan B end fraction equals a rightwards double arrow fraction numerator b over denominator tan A. tan B end fraction equals a space open parentheses u sin g space left parenthesis 1 right parenthesis close parentheses rightwards double arrow tan A. tan B equals b over a... left parenthesis 3 right parenthesis G i v e n space t h a t space A plus B equals C rightwards double arrow tan open parentheses A plus B close parentheses equals tan C rightwards double arrow fraction numerator tan A plus tan B over denominator 1 minus tan A tan B end fraction equals tan C rightwards double arrow fraction numerator b over denominator 1 minus begin display style b over a end style end fraction equals tan C space open parentheses u sin g space left parenthesis 1 right parenthesis space a n d space left parenthesis 3 right parenthesis close parentheses rightwards double arrow fraction numerator a b over denominator a minus b end fraction equals tan C T h e space a b o v e space e q u a t i o n space r e l a t e s space tan C space w i t h space apostrophe a apostrophe space a n d space apostrophe b apostrophe. space A space a n d space B space a r e space e l i m i n a t e d. space

Answered by satyajit samal | 13th May, 2015, 12:52: PM

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