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Q.
The number of integers in the domain of $f ( x )=\frac{1}{\sqrt{\ln \left(\cos ^{-1} x \right)}}$, is
Inverse Trigonometric Functions
Solution:
We have $f(x)=\frac{1}{\sqrt{\ln \cos ^{-1} x}}$
For domain of $f ( x ), \ln \left(\cos ^{-1} x \right)>0 \Rightarrow \cos ^{-1} x >1$ and $\cos ^{-1} x \leq \pi$ $\Rightarrow \cos \pi \leq x \leq \cos 1 \Rightarrow-1 \leq x< \cos 1$.
Hence number of integers in the domain of $f ( x )$ are 2 i.e., -1 and 0 .