prove that

(i) sin^-1 (12/13) + cos^-1 (4/5) +tan^-1 (63/16)=0

(ii) 2sin^-1(3/5) - tan^-1 (17/31) =pi / 4

solve:

cos^-1 ([x²-1]/[x²+1]) + tan^-1[(2x)/(x²-1)]=2pi/3

(cosx - cosy)² + (sinx - siny)² = 4 sin²(x-y)/2.

solve for x
cos(2sin^-1x) =1/9 ,x>0