Answer with Step-by-step explanation:
We are given that
We have to prove that why the limit x approaches 0(csc(x)-cot(x)) involves an indeterminate form and prove that the limit equals to 0.
Because and
We know that cos 0=1 and sin 0=0
Substitute the values then we get
We know that is indeterminate form
Hence, the limit x approaches 0(csc(x)-cot(x)) involves an indeterminate form.
L'hospital rule:Apply this rule and differentiate numerator and denominator separately when after applying we get indeterminate form
Now,using L' hospital rule
because
Now, we get
Hence,