Question

sin^-1(2x/1+x^2)+cos^-1(1-x^2/1+x^2)​

Answer 1

Answer:

sin[tan−11−x22x+ cos−11−x21+x2] Let x = tanθ So tan−11−x22x = tan−11−tan2θ2tanθ =tan−1 [cos2θ−sin2θ2sinθcosθ] =tan−1[cot2θ] = tan−1[tan(π2−2θ)] =π2−2θcos−11−x21+x2 =cos−11−tan2θ1+tan2θ =cos−1[cos2θ−sin2θcos2θ+sin2θ] =cos−1[cos2θ] = 2θsin[tan−11−x22x+ cos−11−x21+x2] =sin[π2