What is the formula of (1 - cos x) / sin x?

Solution:

As we know that (1 - cos x) = 2sin² (x/2) and sin x = 2sin (x/2).cos (x/2)

(1 - cos x) = 2sin² (x/2) ---- (1)

sin x = 2sin (x/2).cos (x/2) ---- (2)

(1 - cos x) / sinx = 2sin² (x/2) / 2sin (x/2).cos (x/2) [From (1) and (2)]

On taking 2sin (x/2) common and cancelling, we get

(1 - cos x) / sinx = sin (x/2) / cos (x/2)

= tan (x/2)   [ ∵ tan x = sin x / cos x]

Thus, (1 - cos x) / sin x = tan (x/2)

What is the formula of (1 - cos x) / sin x?

Summary:

The formula of (1 - cos x) / sin x = tan (x/2)