Evaluate the limit of the difference sin x-cosx, if x goes to to pi/2?
The value of lim x--> pi/2 [ sin x - cos x] is required.
We know that sin (pi/2) = 1 and cos (pi/2) = 0
So we can just substitute x = pi/2
sin x - cos x
=> 1 - 0
The required limit is 1.
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.