Evaluate the following: ^ -1 ( 6 7 ) - Vidyadip

Question

Evaluate the following:
$\tan^{-1}\Big(\tan\frac{6\pi}{7}\Big)$

✓

Answer

We know that $\tan^{-1}(\tan\theta)=\theta,-\frac{\pi}{2}<\theta<\frac{\pi}{2}$We have
$\tan^{-1}\Big(\tan\frac{6\pi}{7}\Big)$
$=\frac{6\pi}{7}-\pi$ $\Big(\because\ \tan^{-1}(\tan\theta)=\theta-\pi,\ \text{if }\theta\in\Big(\frac{\pi}{2},\frac{3\pi}{2}\Big)\Big)$ $=-\frac{\pi}{7}$

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 "1 Marks Question" 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

Compute $\text{P}(\text{A}|\text{B})\ \text{if}\ \text{P}(\text{B})=0.5\ \text{and}\ \text{P}(\text{A}\cap\text{B})=0.32$

Determine whether or not each of the definition of $*$ given below gives a binary operation. In the event that $*$ is not a binary operation, give justification for this. On $Z^+,$ define $*$ by $a ^* b = ab$

If P(A) = $\frac{6}{11}$, P(B) = $\frac{5}{11}$ and $\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{7}{11}$, find P(A|B)

Determine order and degree (if defined) of differential equation ${\left( {\frac{{ds}}{{dt}}} \right)^4} + 3s\frac{{{d^2}s}}{{d{t^2}}} = 0$

Find the value of $\int \frac{1}{x} d x$ :

Classify the following measures as scalar and vector:
10 meters south-east.

Construct a 4 × 3 matrix whose element are:
$\text{a}_\text{ij}=2\text{i}+\frac{\text{i}}{\text{j}}$

Given an example of:
A triangular matrix.

Define degree of a differential equation.

Determine order and degree $($if defined$)$ of differential equation $\left(y^{\prime \prime \prime}\right)^{2}+\left(y^{\prime \prime}\right)^{3}+\left(y^{\prime}\right)^{4}+y^{5}=0$