Let ^ - 1 ( 5 4 ) = , ^ - 1 ( - 2 3 ) = Then :- - Vidyadip

MCQ

Let ${\tan ^{ - 1}}\left( {\tan \frac{{5\pi }}{4}} \right) = \alpha ,{\tan ^{ - 1}}\left( { - \tan \frac{{2\pi }}{3}} \right) = \beta $ Then :-

A
$\alpha > \beta$
✓
$4 \alpha -3 \beta = 0$
C
$\alpha + \beta = \frac{5 \pi}{12}$
D
None

✓

Answer

Correct option: B.

$4 \alpha -3 \beta = 0$

b
given, $\alpha=\tan ^{-1}\left(\tan \frac{5 \pi}{4}\right)$

$=\tan ^{-1}\left(\tan \left(\pi+\frac{\pi}{4}\right)\right)$

$=\tan ^{-1}\left(\tan \left(\frac{\pi}{4}\right)\right)$

$=\frac{\pi}{4}$

$\Rightarrow 4 \alpha=\pi$

$\beta=\tan ^{-1}\left(-\tan \frac{2 \pi}{3}\right)$

$=\tan ^{-1}\left(-\tan \left(\pi-\frac{\pi}{3}\right)\right)$

$=\tan ^{-1}\left(\tan \left(\frac{\pi}{3}\right)\right)$

$=\frac{\pi}{3}$

$\Rightarrow 3 \beta=\pi \quad \ldots \ldots$

From (1) and (2) we have

$\therefore 4 \alpha=3 \beta$

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 STD 12 - 2. inverse trigonometric function→STD 12 - 2. inverse trigonometric function — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Which of the following function $(s)$ not defined at $x = 0$ has/have removable discontinuity at $x = 0$ ?

If $ |a|=|b| $ then $ (a+b).(a-b) $ is

The degree of the differntial equation $\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big)^{2}=\Big(\frac{\text{dy}}{\text{dx}}\Big)=\text{y}^{3}$ is:

The area bounded by the curve $y = x^2 + 1\,$ and the tangents to it drawn from the origin is

The function f : R → R defined by f(x) = (x - 1)(x - 2)(x - 3) is:

If the volume of a spherical balloon is increasing at the rate of $ 900$ $cm^3$ $per\, sec$ , then the rate of change of radius of balloon at instant when radius is $ 15\,cm$ [ in $cm/sec$ ]

Let $[t]$ denote the largest integer less than or equal to $t$. If

$\int_0^3\left(\left[x^2\right]+\left[\frac{x^2}{2}\right]\right) d x=a+b \sqrt{2}-\sqrt{3}-\sqrt{5}+c \sqrt{6}-\sqrt{7},$ where $a, b, c \in z$, then $a+b+c$ is equal to.........

Let $\Delta$ be the area of the region $\left\{( x , y ) \in R ^2: x ^2+ y ^2 \leq 21, y ^2 \leq 4 x , x \geq 1\right\}$. Then $\frac{1}{2}\left(\Delta-21 \sin ^{-1} \frac{2}{\sqrt{7}}\right)$ is equal to

The value of $\int \cot 2 x\ d x$ will be

If $m$ and $\sigma ^2$ are the mean and variance of random variable $x$, whose distribution is given by

$\begin{array}{|l|l|l|l|l|l|} \hline X=x & 0 & 1 & 2 & 3 & 4 \\ \hline P(X=x) & \frac{1}{3} & \frac{1}{2} & 0 & \frac{1}{6} & 0 \\ \hline \end{array}$

, then