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

2 Answers | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

=> 1

The required limit is 1.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

We’ve answered 318,991 questions. We can answer yours, too.

Ask a question