IF 'A' AND 'B' ARE ACUTE ANGLES SUCH THAT TAN A=1/2 AND TAN B = 1/3 AND (TAN A+B) = TAN A = TAN B/ 1- TAN A* TAN B ,THEN FIND "A + B"?

Asked by Sai Seravan Bodipudi | 24th Jun, 2014, 11:46: AM

Expert Answer:

G i v e n space t h a t space tan A equals 1 half space a n d space tan B equals 1 third W e space k n o w space t h a t comma space tan open parentheses A plus B close parentheses equals fraction numerator tan A plus tan B over denominator 1 minus tan A tan B end fraction T h e r e f o r e comma space space tan open parentheses A plus B close parentheses equals fraction numerator 1 half plus 1 third over denominator 1 minus open parentheses 1 half cross times 1 third close parentheses end fraction rightwards double arrow space tan open parentheses A plus B close parentheses equals fraction numerator 5 over 6 over denominator 1 minus 1 over 6 end fraction rightwards double arrow space tan open parentheses A plus B close parentheses equals fraction numerator 5 over 6 over denominator 5 over 6 end fraction rightwards double arrow space tan open parentheses A plus B close parentheses equals 1 rightwards double arrow tan open parentheses A plus B close parentheses equals tan straight pi over 4 rightwards double arrow A plus B equals straight pi over 4

Answered by Vimala Ramamurthy | 25th Jun, 2014, 08:55: AM

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