2 tan B + cot B = tan A , show that 2 tan(A-B) = cot B

Asked by agarwalharsh8476 | 6th Aug, 2019, 08:32: PM

Expert Answer:

2 tan left parenthesis A minus B right parenthesis equals 2 open parentheses fraction numerator tan A minus tan B over denominator 1 plus tan A space tan B space end fraction close parentheses
equals 2 open parentheses fraction numerator 2 tan B plus c o t B minus tan B over denominator 1 plus open parentheses 2 tan B plus c o t B close parentheses space tan B end fraction close parentheses space space space...... space space S i n c e space tan A equals 2 tan B plus c o t B
equals 2 open parentheses fraction numerator tan B plus c o t B over denominator 1 plus 2 tan squared B plus c o t B space tan B end fraction close parentheses
equals 2 open parentheses fraction numerator c o t B open parentheses tan squared B plus 1 close parentheses over denominator 1 plus 2 tan squared B plus 1 end fraction close parentheses
equals 2 open parentheses fraction numerator c o t B open parentheses tan squared B plus 1 close parentheses over denominator 2 open parentheses 1 plus tan squared B close parentheses end fraction close parentheses
equals c o t B
H e n c e comma space 2 tan left parenthesis A minus B right parenthesis equals c o t B

Answered by Renu Varma | 7th Aug, 2019, 10:24: AM