For the principal values, evaluate the following: ^ -1 ( 3 )- ^ -… - Vidyadip

Question

For the principal values, evaluate the following:
$\tan^{-1}\big(\sqrt3\big)-\sec^{-1}(-2)$

✓

Answer

Let $\tan^{-1}\big(\sqrt3\big)=\text{x}.$ Then, $\tan\text{x}=\sqrt3=\tan\Big(\frac{\pi}{3}\Big)$
$\therefore\tan^{-1}\big(\sqrt3\big)=\frac{\pi}{3}$
Let $\sec^{-1}(-2)=\text{y}.$ Then, $\sec\text{y}=-2=\sec\Big(\pi-\frac{\pi}{3}\Big)$
$\therefore\sec^{-1}(-2)=\frac{2\pi}{3}$
$\therefore\tan^{-1}\big(\sqrt3\big)-\sec^{-1}(-2)=\frac{\pi}{3}-\frac{2\pi}{3}$
$=\frac{\pi-2\pi}{3}=-\frac{\pi}{3}$

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 "3 Marks" 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

Prove that the function f : N → N, defined by f(x) = x² + x + 1 is one-one but not onto. Find inverse of f : N → S, where S is range of f.

Tickets are numbered from 1 to 10. Two tickets are drawn one after the other at random. Find the probability that the number on one of the tickets is a multiple of 5 and on the other a multiple of 4.

Evaluate the following integrals:
$\int\text{e}^{\text{x}}(\cos\text{x}-\sin\text{x})\text{dx}$

Evaluate the following integrals:

$\int\frac{\cos2\text{x}}{\sqrt{\sin^22\text{x}+8}}\text{ dx}$

Evaluate the following:
$\int\sqrt{5-2\text{x}+\text{x}^2}\text{dx}$

Find the vector from the origin O to the centroid of the triangle whose vertices are (1, -1, 2), (2, 1, 3) and (-1, 2, -1).

Find the value of the determinant $\begin{vmatrix}101&102&103\\104&105&106\\107&108&109\end{vmatrix}$

Differentiate the following functions with respect to x:
$(\log\sin\text{x})^2$

Find the vector equation of the line passing through the point A(1, 2, -1) and parallel to the line 5x - 25 = 14 - 7y = 35z.

Solve:
$\sin\Big(\sin^{-1}\frac{1}{5}+\cos^{-1}\text{x}\Big)=1$