If a and b are acute angles such that tan a=1/3 tan b = 1/2 and tan A+B = 45

Asked by ommkardas2004 | 9th Jun, 2020, 05:54: AM

Expert Answer:

Question should be:
If a and b are acute angles such that tan a=1/3 and tan b = 1/2 then prove that a+b = 45o
Solution:

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 third end style space plus begin display style 1 half end style space over denominator 1 space minus space begin display style 1 third end style cross times begin display style 1 half 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 Renu Varma | 9th Jun, 2020, 09:23: AM