Question

If f(x) = sinx +cosx
Then f(x)+f(-x)
f(x)-f(-x)
​

Answer 1

We know, [p] is discontinuous at integral values of p.

Now, sinx+cosx = √2sin(x+π/4)

So, [sinx+cosx] = [√2sin(x+π/4)]-will be discontinuous at integral values of √2sin(x+π/4) in the interval (0,2π).

at x = π/2 ,3π/4 , π, 3π/2 , 7π/4; the value of √2sin(x+π/4) is an integer. (Verify)

Now, by inspection, we find that,

So, there are 5 points in the interval (0,2π), for which [sinx+cosx] is discontinuous. (Ans)

Hope, you'll understand..!!

Thank You!