Find the domain of each of the following functions given by (i) (ii)

Solution:

(i)

f(x)=11–cosx
\mathrm{f}(\mathrm{x})=\frac{1}{\sqrt{1-\cos \mathrm{x}}}

As per the question,

It is known that the value of lies between

Multiply by negative sign, we have

Or

When we add 1, we have

(i)

So now,

Or,

As a result, the domain of

(ii)

As per the question,

For real value of ,

When

When

Therefore, , to satisfy the provided equation.

As a result, the domain of