Question

`lim_("x"-> 0) ("cosec x - cot x")/"x"`  is equal to ____________.

Options

• 0

• `1/2`

• None of these

• 1

Answer 1

`lim_("x"-> 0) ("cosec x - cot x")/"x"`  is equal to `underline(1/2)`.

Explanation:

`=  lim_("x"-> 0) ("cosec x - cot x")/"x"`

`=  lim_("x"-> 0) (1 - "cos x")/("x sin x")`

`=  lim _ ("x" -> 0) ((1 - "cos x")( 1 = "cos x"))/("x sin x" (1 + "cos x"))`

`=  lim_("x" -> 0) "sin x"/"x". 1/(1 + "cos x")`

` = 1/2`