Tan^-1(x^1/2)=1/2cos^-1(1-x/1+x),x E [0,1]

Asked by Balbir | 28th Apr, 2017, 05:50: PM

Expert Answer:

begin mathsize 16px style RHS equals 1 half cos to the power of negative 1 end exponent open parentheses fraction numerator 1 minus straight x over denominator 1 plus straight x end fraction close parentheses
square root of straight x equals tanθ space rightwards double arrow straight theta equals tan to the power of negative 1 end exponent square root of straight x
RHS equals 1 half cos to the power of negative 1 end exponent open parentheses fraction numerator 1 minus tan squared straight theta over denominator 1 plus tan squared straight theta end fraction close parentheses
equals 1 half cos to the power of negative 1 end exponent open parentheses cos 2 straight theta close parentheses
equals 1 half cross times 2 straight theta
equals straight theta
equals tan to the power of negative 1 end exponent square root of straight x end style

Answered by Sneha shidid | 29th Apr, 2017, 02:09: PM