Evaluate the following: ( ^ -1 24 7 ) - Vidyadip

Question

Evaluate the following:
$\cos\Big(\tan^{-1}\frac{24}{7}\Big)$

✓

Answer

$\cos\Big(\tan^{-1}\frac{24}{7}\Big)$
$=\cos\begin{bmatrix}\cos^{-1}\frac{1}{\sqrt{1+\big(\frac{24}{7}\big)^2}}\end{bmatrix}$ $\bigg[\because\ \tan^{-1}\text{x}=\cos^{-1}\frac{1}{\sqrt{1+\text{x}^2}}\bigg]$
$=\cos\begin{bmatrix}\cos^{-1}\frac{1}{\sqrt{1+\frac{576}{49}}}\end{bmatrix}$
$=\cos\bigg[\cos^{-1}\frac{1}{\frac{25}{7}}\bigg]$
$=\cos\Big[\cos^{-1}\frac{7}{25}\Big]$
$=\frac{7}{25}$

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

In a legislative assembly election, a political group hired a public relations firm to promote its candidates in three ways: telephone, house calls and letters. The cost per contact (in paise) is given matrix A as. $\ \ \ \ \ \ \ \ \ \ \ \ \text{Cost per contact}\\\text{A}=\begin{bmatrix}40&\text{Telephone}\\100&\text{House call}\\50&\text{Letter}\end{bmatrix}$The number of contacts of each type made in two cities X and Y is given in matrix B as
$\text{BA}=\begin{bmatrix}\text{Telephone}&\text{House call}&\text{Letter}\\1000&500&5000\\3000&1000&10000\end{bmatrix} \begin{matrix}\rightarrow\text{X}\\\rightarrow\text{Y}\end{matrix}$
Find the total amount spent by the group in the two cities X and Y.

Let * be a binary operation on Z defined by a * b = a + b - 4 for all a, b ∈ Z.
Find the invertible elements in Z.

Find the value of $\cos ^{-1} \frac{1}{2}+2 \sin ^{-1} \frac{1}{2}$.

Find the maximum value of $\begin{vmatrix}1&1&1\\1&1+\sin\theta&1\\1&1&1+\cos\theta \end{vmatrix}$

If $\text{x}=\text{f}(\text{t})$ and $\text{y}=\text{g}(\text{t}),$ then write the value of $\frac{\text{d}^2\text{y}}{\text{dx}^2}.$

For the principal values, evaluate the following:
$\tan^{-1}(-1)+\cos^{-1}\Big(-\frac{1}{2}\Big)$

Show that the vector $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ is equally inclined with the axes OX, OY and OZ.

Find the area of the parallelogram whose adjacent sides are determined by the vectors $\vec{a}=\hat{i}-\hat{j}+3 \hat{k}$ and $\vec{b}=2 \hat{i}-7 \hat{j}+\hat{k}$.

Let the vectors $\vec{a},\vec{b},\vec{c}$ be given as $a_{1}\hat{i}+a_{2}\hat{j}+a_{3}\hat{k},\ b_{1}\hat{i}+b_{2}\hat{j}+b_{3}\hat{k},$ $c_{1}\hat{i}+c_{2}\hat{j}+c_{3}\hat{k}.$ Then show that $\vec{a}\times(\vec{b}+\vec{c})=\vec{a}\times\vec{b}+\vec{a}\times\vec{c}.$

Differentiate the function ${\left( {x\cos x} \right)^x} + {\left( {x\sin x} \right)^{\frac{1}{x}}}$ w.r.t. x.