Evaluate the following limits in Exercises 1 to 22: limₓ→₀ (cosec x - cot x)

Solution:

At x = 0, the value of the given function takes the form ∞-∞, which is an indeterminate form.

So we will evaluate the given limit differently.

Now,

limₓ→₀ (cosec x - cot x)

= limₓ→₀ (1/sinx - cosx/sinx)

= limₓ→₀ (1 - cosx)/sinx

Divide the numerator and denominator by x,

= limₓ→₀ [(1 - cosx)/x] / (sinx/x)

= [limₓ→₀ [(1 - cosx)] / [limₓ→₀ (sinx/x)]

= 0/1 [∵ limₓ→₀ (1 - cosx)/x = 0 and limₓ→₀ (sinx/x) = 1]

= 0

NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 21

Evaluate the following limits in Exercises 1 to 22: limₓ→₀ (cosec x - cot x)

Summary:

The value of the limit limₓ→₀ (cosec x - cot x) is 0