^ -1 3+ ^ -1 = ^ -1 (3+ 1-3 ) is valid for what values of ? - Vidyadip

MCQ

$\tan ^{-1} 3+\tan ^{-1} \lambda=\tan ^{-1}\left(\frac{3+\lambda}{1-3 \lambda}\right)$ is valid for what values of $\lambda ?$

A
$\lambda \in\left(-\frac{1}{3}, \frac{1}{3}\right)$
B
$\lambda > \frac{1}{3}$
✓
$\lambda < \frac{1}{3}$
D
All real values of $\lambda$

✓

Answer

Correct option: C.

$\lambda < \frac{1}{3}$

$\text {Given, } \tan ^{-1} 3+\tan ^{-1} \lambda$
$=\tan ^{-1}\left(\frac{3+\lambda}{1-3 \lambda}\right)$
$\tan ^{-1} 3+\tan ^{-1} \lambda$
$=\tan ^{-1}\left(\frac{3+\lambda}{1-3 \lambda}\right) \text { for } 3 \lambda < 1$
$\therefore 3 \lambda < 1$
$\Rightarrow \lambda < \frac{1}{3}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The determinant $\left| {\,\begin{array}{*{20}{c}}a&b&{a - b}\\b&c&{b - c}\\2&1&0\end{array}\,} \right|$ is equal to zero if $a,b,c$ are in

The length of the perpendicular drawn from the point (4, -7, 3) on the y-axis is:

If $\theta$ is the angle between two vectors $\vec{a}$ and $\vec{b},$ then $\vec{a} \cdot \vec{b} \geq 0$ only when

In a box containing $100$ eggs, $10$ eggs are rotten. The probability that out of a sample of $5$ eggs none is rotten if the sampling is with replacement is

Let $L$ denote the set of all straight lines in a plane. Let a relation $R$ be defined by $\alpha R\beta \Leftrightarrow \alpha \bot \beta ,\,\alpha ,\,\beta \in L$. Then $R$ is

$\int\sec^2\text{x}.\text{cosec}^2\text{xdx}=$

$\int_{\,0}^{\,1000} {{e^{x - [x]}}dx} $ is

For which of the following values of $m$, the area of the region bounded by the curve $y = x - {x^2}$ and the line $y = mx$ equals $\frac{9}{2}$

The Image of the point $(2, -1, 5)$ in the plane $\vec{\text{r}},\hat{\text{i}}=0$ is :

$\int_{0}^{\frac{\pi^2}{4}}\frac{\sin\sqrt{\text{y}}}{\sqrt{\text{y}}}.$