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

By BYJU'S Exam Prep

Updated on: September 11th, 2023

We know that,

(1 – cos x) = 2sin² (x/2) …. (1)

sin x = 2sin (x/2).cos (x/2) ….(2)

And it is asked in the question, What is the formula of (1 – cos x)/ sin x?

and to find out the same,

Table of content

Dividing (2) by (1)

(1 – cos x) / sin x = 2sin² (x/2) / 2sin (x/2).cos (x/2)

By taking 2 sin (x/2) as common

(1 – cos x)/sin x = sin (x/2)/cos (x/2)

As sin x/ cos x = tan x

(1 – cos x)/sin x = tan (x/2)

Therefore, when asked What is the formula of (1 – cos x)/ sin x? then the answer will be the formula of (1 – cos x)/sin x = tan (x/2)

Summary:

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

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