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 "Solve the Following Question.(2 Marks)" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

A bag contains 8 marbles of which 3 are blue and 5 are red. One marble is drawn at random, its cooler is noted and the marble is replaced in the bag. A marble is again drawn from the bag and its colour is noted. Find the probability that the marble will be,
Blue followed by red.

Find the values of $\lambda$ for which the angle between the vectors $\vec{a}=2 \lambda^2 \hat{i}+4 \lambda \hat{j}+\hat{k}$ and $\vec{b}=7 \hat{i}-2 \hat{j}+\lambda \hat{k}$

The following defines a relation on N:
x + 4y = 10, $\text{x, y}\in\text{N}$
Determine which of the above relations are reflexive, symmetric and transitive.

Find the area of the parallelogram whose adjacent sides are the vectors $\bar{a}=2 \hat{i}-2 \hat{j}+\hat{k}$

and $\bar{b}=\hat{i}-3 \hat{j}-3 \hat{k}$.

Find the area of the region bounded by the curve $y=x^2$ and the line $y=4$.

If $\begin{bmatrix}\text{a+b}&2\\5&\text{b} \end{bmatrix}=\begin{bmatrix}6&5\\2&2 \end{bmatrix}$, then find a.

Find the measure of the acute angle between the lines represented by: $2 x^2+7 x y+3 y^2=0$

Evaluate the following integrals:
$\int\bigg (2^{\text{x}}+\frac{5}{\text{x}}-\frac{1}{\text{x}^{\frac{1}{3}}}\bigg)\text{dx}$

With usual notations, prove that $\frac{\cos A }{ a }+\frac{\cos B }{ b }+\frac{\cos C }{ c }=\frac{ a ^2+ b ^2+ c ^2}{2 abc }$

If A is a square matrix such that A (adj A) = 5I, where I denotes the identity matrix of the same order. Then, find the value of |A|.