Verify the identity.

sin (x+pi/2)=cos x

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

sin (x+pi/2)=cos x

The most important subsets of the set of real numbers include the rational and the irrational numbers. The set of rational numbers can be divided into further subsets, including the natural numbers, the whole numbers and the integers.

Step-by-step explanation: