Download App

Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
Question
Evaluate the following:
$\tan^{-1}(\tan4)$
✓

Answer

We know that
$\tan^{-1}(\tan\theta)=\theta,-\frac{\pi}{2}<\theta<\frac{\pi}{2}$
We have
$\tan^{-1}(\tan4)$
$=4-\pi$ $\Big(\because\ \tan^{-1}(\tan\theta)=\theta-\pi,\text{if }\theta\in\Big(\frac{\pi}{2},\frac{3\pi}{2}\Big)\Big)$

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 "1 Marks Question" 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

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\sqrt{1-\text{y}^2}\text{dx}+\sqrt{1-\text{x}^2}\text{dx}=0$
→
Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{d}^2\text{y}}{\text{dx}^2}+5\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)-6\text{y}=\log\text{x}$
→
Write the differential equation obtained emliminating the arbitrary constant $C$ in the equation $xy = C^2$.
→
Write the order of the differential equation of the family of circles touching X-axis at the origin.
→
Find the area enclosed by curve $|x|+|y|=1$.
→
A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B?
→
If the vectors $a \hat{i}-a \hat{j}+\hat{k}$ and $a \hat{i}+\hat{j}-2 \hat{k}$ are perpendicular to each other, then find the value of $a$.
→
Two coins are tossed once, determine P(E|F), where E: tail appears on one coin, F: one coin shows head.
→
For a $2 \times 2$ matrix, $A=\left[a_{i j}\right]$, whose elements are given by $a_{i j}=\frac{i}{j}$, write the value of $a_{12}$.
→
Find the value of the expression ${\tan ^{ - 1}}\left( {\tan \frac{{3\pi }}{4}} \right)$.
→