47
The result $\tan ^{-1} x-\tan ^{-1} y=\tan ^{-1}\left(\frac{x-y}{1+x y}\right)$ is true when the value of $x y$ is ............ .
Explanation
$$\begin{aligned} \text{We know that,}\quad\tan ^{-1} x-\tan ^{-1} y & =\tan ^{-1}\left(\frac{x-y}{1+x y}\right) \\ \text{ where,}\quad x y & >-1 \end{aligned}$$
48
The value of $\cot ^{-1}(-x) x \in R$ in terms of $\cot ^{-1} x$ is ............ .
Explanation
We know that,
$$\cot ^{-1}(-x)=\pi-\cot ^{-1} x, x \in R$$
49
All trigonometric functions have inverse over their respective domains.
A
TRUE
B
FALSE
50
The value of the expression $\left(\cos ^{-1} x\right)^2$ is equal to $\sec ^2 x$.
A
TRUE
B
FALSE
51
The domain of trigonometric functions can be restricted to any one of their branch (not necessarily principal value) in order to obtain their inverse functions.
A
TRUE
B
FALSE