Posted by Tom on Sunday, June 17, 2012 at 10:32am.
cos(x+pi/2) = cosx cos pi/2 - sinx sin pi/2 = 0 - sinx = -sinx so limit cos(x+pi/2)/x as x----> o = lim -sinx/x , x ---> 0 = -1 using the fact that lim sinx/x = 1