Download App

INVERSE TRIGNOMETRIC FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINVERSE TRIGNOMETRIC FUNCTIONS1 Mark
Question
Write the principal value of $\tan^{-1}(\sqrt{3}) - \cot^{-1}( - \sqrt{3}).$
✓

Answer

$\tan^{-1}\sqrt{3} - \cot^{-1}(- \sqrt{3}) = \tan^{-1}\bigg(\tan\frac{\pi}{3}\bigg) -\cot^{-1}\bigg(- \cot\frac{\pi}{6}\bigg)$
$ =\tan^{-1}\bigg(\tan\frac{\pi}{3}\bigg) - \cot^{-1}\bigg(\cot\bigg(\pi - \frac{\pi}{6}\bigg)\bigg)$
$ = \tan^{-1}\bigg(\tan\frac{\pi}{3}\bigg) - \cot^{-1}\bigg(\cot\frac{5\pi}{6}\bigg)$
$ = \frac{\pi}{3} - \frac{5\pi}{6}\bigg[\because\frac{\pi}{3}\in\bigg( -\frac{\pi}{2} , \frac{\pi}{2}\bigg)\text{ and }\frac{5\pi}{6}\in(0,\pi)\bigg]$
$ = \frac{2\pi - 5 \pi}{6} = - \frac{\pi}{2}.$

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 TRIGNOMETRIC FUNCTIONS→INVERSE TRIGNOMETRIC FUNCTIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Show that the function f: N $ \to $ N given by f (1) = f (2) = 1 and f (x) = x - 1, for every x > 2, is onto but not one-one.
→
Integrate the functions in Exercises:
$\frac{1}{\text{x}-\sqrt{\text{x}}}$
→
Write the order and the degree of the following differential equation:
$\text{x}^3\Big(\frac{\text{d}^2\text{y}}{\text{dx}^2}\Big)^2+\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^4=0$
→
Find the principal value of $\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)$
→
Find $ \int ( \sqrt { \cot x } + \sqrt { \tan x } )$dx
→
Find the rate of change of the area of a circular disc with respect to its circumference when the radius is 3cm.
→
If $\vec a$ and $\vec b$ are two collinear vectors, then which of the following are incorrect:
→
Find the principal value of $cosec^{-1}(-\sqrt{2})$.
→
If the matrix A is both symmetric and skew symmetric, then
→
Find the direction cosines of the following vector: $2\hat{\text{i}}+2\hat{\text{j}}-\hat{\text{k}}$
→