Find the domain of each of the following functions given by

Given:

To find: the domain of function

Explanation: So the domain of a function consists of all the first elements of all the ordered pairs, i.e., x, so we have to find the values of x to get the required domain

Given,

We know the value of cos x lies between -1, 1, so

-1≤ cos x≤ 1

Multiplying by negative sign, we get

Or 1≥- cos x≥ -1

Adding with 1, we get

2≥1- cos x≥0…………(i)

Now for real value of

1- cos x≠0

⇒ cos x≠ 1

Or, x≠2nπ ∀n∈Z

Hence the domain of f = R-{2nπ:n∈Z}