Evaluate the following: ( ^ -1 8 17 ) - Vidyadip

Question

Evaluate the following:
$\tan\Big(\cos^{-1}\frac{8}{17}\Big)$

✓

Answer

$\tan\Big(\cos^{-1}\frac{8}{17}\Big)$
$=\begin{Bmatrix}\tan^{-1}\frac{\sqrt{1-\Big(\frac{8}{17}\Big)^2}}{\frac{8}{17}}\end{Bmatrix}$ $\bigg[\because\ \cos^{-1}\text{x}=\tan^{-1}\bigg(\frac{\sqrt{1-\text{x}^2}}{\text{x}}\bigg)\bigg]$
$=\tan\Bigg(\tan^{-1}\frac{\frac{15}{17}}{\frac{8}{17}}\Bigg)$
$=\frac{15}{8}$

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" 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

If A is a square matrix such that |A| = 2, write the value of $\big|\text{A}\text{A}^{\text{T}}\big|.$

Find the values of x, y and z from the following equations:
$\begin{bmatrix}\text{x+y} & 2 \\5+\text{z} & \text {xy} \end{bmatrix}=\begin{bmatrix}6 & 2 \\5& 8 \end{bmatrix}$

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{d}^3\text{x}}{\text{dt}^3}+\frac{\text{d}^3\text{x}}{\text{dt}^2}+\Big(\frac{\text{ dx}}{\text{dt}}\Big)^2=\text{e}^\text{t}$

Evaluate the following integrals:

$\int\cos\sqrt{\text{x}}\text{dx}$

Evaluate $\cos\Big[\cos^{-1}\Big(\frac{-\sqrt{3}}{2}\Big)+\frac{\pi}{6}\Big]$

Find the domain of the following functions:
^{$\text{f(x)}=\sin^{-1}\text{x}^2$}

For what value of 'a' the vectors $2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}$ and $\text{a}\hat{\text{i}}+6\hat{\text{j}}-8\hat{\text{k}}$ are collinear?

Write the coordinate axis to which the line $\frac{\text{x}-2}{3}=\frac{\text{y}+1}{4}=\frac{\text{z}-1}{0}$ is perpendicular.

Determine whether the below relation is reflexive, symmetric and transitive:
Relation R in the set A of human beings in a town at a particular time given by
R = {(x, y) : x and y work at the same place}

Express matrix as the sum of a symmetric and a skew-symmetric matrix: $\left[\begin{array}{rr} {1} & {5} \\ {-1} & {2} \end{array}\right]$