given data sin (x+pi/2)=cos x now using sin law sin(a+b)=sin(a)cos(b)+cos(a)sin(b) now using above values sin(pi/2+x)=sin(pi/2)cos(x)+cos(pi/2)sin(x) as we know that sin(pi/2)=1 cos(pi/2)=0 now putting these values sin(pi/2+x)=1*cosx+0*1 sin(pi/2+x)=cosx hence proved that
