Question

`lim_("x" -> 0) (1 - "cos x")/"x sin x"` is equal to ____________.

Options

• 1

• `1/2`

• 0

• 2

Answer 1

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

Explanation:

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

`=  lim_("x" -> 0) (1 - "cos"^2 "x")/("x sin x" (1 + "cos x")) lim_("x" -> 0) "sin x"/"x" . 1/(1 + "cos x")`

`= 1. 1/(1+ 1)`

`= 1/2`