Evaluate the limit of the difference sin x-cosx, if x goes to to pi/2?

We'll evaluate the limit of the given difference as it
follows:

lim (sin x - cos x) = lim sin x - lim cos x,
x-> pi/2

We'll replace x by the value of pi/2 and
we'll get:

lim sin x - lim cos x = lim sin pi/2 - lim cos
pi/2

sin pi/2 = 1

cos pi/2 =
0

lim sin x - lim cos x = lim 1 - lim
0

By definition, the limit of a constant is the value of
the constant:

lim sin x - lim cos x = 1 -
0

Therefore, if x approaches to pi/2, 
lim (sin x - cos x) = 1.