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ICSE Class 10 Answered

If a and b are acute angles such that tan a =1/2,tan b=1/3 and tan(a+b)=tan a +tan b/1-tana*tanb then find tan(a+b)
Asked by kmondaldgms | 17 Aug, 2018, 12:03: AM
answered-by-expert Expert Answer
begin mathsize 16px style We space have space tan left parenthesis straight a space plus space straight b right parenthesis space equals space fraction numerator tana space plus space tanb over denominator 1 space minus space tana cross times tanb end fraction
rightwards double arrow tan left parenthesis straight a space plus space straight b right parenthesis space equals space fraction numerator begin display style 1 half end style space plus begin display style 1 third end style space over denominator 1 space minus space begin display style 1 half end style cross times begin display style 1 third end style end fraction space equals space fraction numerator begin display style 5 over 6 end style over denominator begin display style 5 over 6 end style end fraction space equals space 1
rightwards double arrow tan left parenthesis straight a space plus space straight b right parenthesis space equals space 1
rightwards double arrow tan left parenthesis straight a space plus space straight b right parenthesis space equals space tan space 45 degree space space space...... since space space tan space 45 degree space equals space 1
rightwards double arrow straight a space plus space straight b space equals space 45 degree end style
Answered by Yasmeen Khan | 17 Aug, 2018, 10:50: AM
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