tan^-1x-1/x-2+tan^-1x+1/x+2=pi/4.find value of x. 

 

Asked by sshas3199 | 23rd Aug, 2020, 09:24: PM

Expert Answer:

Given: tan-1(x-1/x-2)+tan-1(x+1/x+2)=pi/4
rightwards double arrow tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style fraction numerator straight x minus 1 over denominator straight x minus 2 end fraction end style plus begin display style fraction numerator straight x plus 1 over denominator straight x plus 2 end fraction end style over denominator 1 minus begin display style fraction numerator straight x minus 1 over denominator straight x minus 2 end fraction end style cross times begin display style fraction numerator straight x plus 1 over denominator straight x plus 2 end fraction end style end fraction close parentheses equals straight pi over 4
rightwards double arrow tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style fraction numerator straight x squared plus straight x minus 2 plus straight x squared minus straight x minus 2 over denominator straight x squared minus 4 end fraction end style over denominator begin display style fraction numerator straight x squared minus 4 minus straight x squared plus 1 over denominator straight x squared minus 4 end fraction end style end fraction close parentheses equals straight pi over 4
rightwards double arrow tan to the power of negative 1 end exponent open parentheses fraction numerator 2 straight x squared minus 4 over denominator negative 3 end fraction close parentheses equals straight pi over 4
rightwards double arrow fraction numerator 2 straight x squared minus 4 over denominator negative 3 end fraction equals tan straight pi over 4 equals 1
rightwards double arrow 2 straight x squared equals 1
rightwards double arrow straight x equals plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction

Answered by Renu Varma | 25th Aug, 2020, 11:25: AM