Evaluate the following: ( ^ -1 12 13 ) - Vidyadip

Question

Evaluate the following:
$\sec\Big(\sin^{-1}\frac{12}{13}\Big)$

✓

Answer

$\sec\Big(\sin^{-1}\frac{12}{13}\Big)$
$=\sec\Bigg[\cos^{-1}\sqrt{1-\Big(\frac{12}{13}\Big)^2}\Bigg]$ $\Big[\because\ \sin^{-1}\text{x}=\cos^{-1}\sqrt{1-\text{x}^2}\Big]$
$=\sec\Big[\cos^{-1}\Big(\sqrt{1-\frac{144}{169}}\Big)\Big]$
$=\sec\Big[\cos^{-1}\Big(\sqrt{\frac{25}{169}}\Big)\Big]$
$=\sec\Big[\cos^{-1}\frac{5}{13}\Big]$
$=\sec\Big[\sec^{-1}\frac{13}{5}\Big]$
$=\frac{13}{5}$

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 "2 Marks Questions" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Write the total number of binary operations on a set consisting of two elements.

A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?

if f(1) = 4, f'(1) = 2, find the value of the derivative of $\log\Big(\text{f}\big(\text{e}^\text{x}\big)\Big)$ w.r.t x at the point x = 0.

Find the principal value of the following:
$\cos^{-1}\Big(-\frac{1}{\sqrt2}\Big)$

Show that the matrix $A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]$ satisfies the equation $A ^2-4 A + I =0$. where $I$ is $2 \times 2$ identity matrix and $O$ is $2 \times 2$ zero matrix. Using this equation, find $A^{-1}$

Prove that $\text{f(x)}=\begin{cases}\frac{\text{x}-|\text{x}|}{\text{x}},&\text{x}\neq0\\2,&\text{x}=0\end{cases}$ is discontinuous at x = 0.

Express $\tan ^{-1}( \frac{\cos x}{1-\sin x}),-\frac{3 \pi}{2}<x<\frac{\pi}{2}$ in the simplest form.

Find the minor of element $6$ in the determinant $\Delta=\left|\begin{array}{lll} {1} & {2} & {3} \\ {4} & {5} & {6} \\ {7} & {8} & {9} \end{array}\right|$

If $x$ and $y$ are connected parametrically by the equations given in Exercise without eliminating the parameter, Find $\frac{\text{dy}}{\text{dx}}.x = 2at^2, y = at^4$

Find the magnitude of two vectors $\vec a$ and $\vec b$, having the same magnitude and such that the angle between them is $60^\circ$ and their scalar product is $\frac{1}{2}$.