find the value of  x

Asked by Kusum and Sanjeet | 11th May, 2016, 09:36: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e q u a t i o n comma
tan to the power of negative 1 end exponent 2 x plus tan to the power of negative 1 end exponent 3 x equals n straight pi plus fraction numerator 3 straight pi over denominator 4 end fraction
Taking space tangent space on space both space the space sides comma space we space have comma
tan open parentheses tan to the power of negative 1 end exponent 2 straight x plus tan to the power of negative 1 end exponent 3 straight x close parentheses equals tan open parentheses nπ plus fraction numerator 3 straight pi over denominator 4 end fraction close parentheses
rightwards double arrow tan open parentheses tan to the power of negative 1 end exponent 2 straight x plus tan to the power of negative 1 end exponent 3 straight x close parentheses equals fraction numerator tan open parentheses nπ close parentheses plus tan open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses over denominator 1 minus tan open parentheses nπ close parentheses cross times tan open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses end fraction
rightwards double arrow tan open parentheses tan to the power of negative 1 end exponent 2 straight x plus tan to the power of negative 1 end exponent 3 straight x close parentheses equals fraction numerator tan open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses over denominator 1 end fraction
rightwards double arrow tan open parentheses tan to the power of negative 1 end exponent 2 straight x plus tan to the power of negative 1 end exponent 3 straight x close parentheses equals negative 1
rightwards double arrow tan open parentheses tan to the power of negative 1 end exponent open parentheses fraction numerator 2 straight x plus 3 straight x over denominator 1 minus 6 straight x squared end fraction close parentheses close parentheses equals negative 1
rightwards double arrow tan open parentheses tan to the power of negative 1 end exponent open parentheses fraction numerator 5 straight x over denominator 1 minus 6 straight x squared end fraction close parentheses close parentheses equals negative 1
rightwards double arrow fraction numerator 5 straight x over denominator 1 minus 6 straight x squared end fraction equals negative 1
rightwards double arrow 5 straight x equals negative 1 plus 6 straight x squared
rightwards double arrow 6 straight x squared minus 5 straight x minus 1 equals 0
rightwards double arrow 6 straight x squared minus 6 straight x plus straight x minus 1 equals 0
rightwards double arrow 6 straight x open parentheses straight x minus 1 close parentheses plus straight x minus 1 equals 0
rightwards double arrow open parentheses 6 straight x plus 1 close parentheses open parentheses straight x minus 1 close parentheses equals 0
rightwards double arrow open parentheses 6 straight x plus 1 close parentheses equals 0 space or space open parentheses straight x minus 1 close parentheses equals 0
rightwards double arrow straight x equals fraction numerator negative 1 over denominator 6 end fraction space or space straight x equals 1

Answered by Vimala | 12th May, 2016, 10:44: AM