Prove that cos(tan-1x) = sin(cot-1x). Please answer as quick as possible with an explanation. Share with your friends Share 1 Vijay Kumar Gupta answered this It is required to prove that, costan-1x=sincot-1xTake the expression on the left hand side. costan-1xSuppose that t=tan-1x, so that tan t=x1 =PBWhere P is perpendicular and B is base of right triangleThen the hypotenuse, H is given by, H=P2+B2=x2+1So the value cos t equals cos t=BH=1x2+1This implies that, t=cos-11x2+1So the left hand side becomes, costan-1x=coscos-11x2+1=1x2+1 .....(1) Take the expression on the right hand side. sincot-1xSuppose that t=cot-1x, so that cot t=x1 =BPWhere P is perpendicular and B is base of right triangleThen the hypotenuse, H is given by, H=P2+B2=x2+1So the value sin t equals sin t=PH=1x2+1This implies that, t=sin-11x2+1So the right hand side becomes, sincot-1x=sinsin-11x2+1=1x2+1 ......(2)From (1) and (2), it is proved that, costan-1x=sincot-1x 0 View Full Answer
