State whether the following is true or false. Justify your answer.
$\cot A$ is not defined for $A = 0^{\circ}$.
$\cot A$ is not defined for $A = 0^{\circ}$.
(TRUE) The statement is true.
We know that $\cot A = \frac{\cos A}{\sin A}$.
For $A = 0^{\circ}$,we have $\cot 0^{\circ} = \frac{\cos 0^{\circ}}{\sin 0^{\circ}}$.
Since $\cos 0^{\circ} = 1$ and $\sin 0^{\circ} = 0$,we get $\cot 0^{\circ} = \frac{1}{0}$.
Division by zero is undefined in mathematics. Therefore,$\cot 0^{\circ}$ is not defined.
We know that $\cot A = \frac{\cos A}{\sin A}$.
For $A = 0^{\circ}$,we have $\cot 0^{\circ} = \frac{\cos 0^{\circ}}{\sin 0^{\circ}}$.
Since $\cos 0^{\circ} = 1$ and $\sin 0^{\circ} = 0$,we get $\cot 0^{\circ} = \frac{1}{0}$.
Division by zero is undefined in mathematics. Therefore,$\cot 0^{\circ}$ is not defined.
Explore More
Similar Questions
State whether the following is true or false. Justify your answer.
$\sin (A+B) = \sin A + \sin B$
$\sin (A+B) = \sin A + \sin B$
Medium
View SolutionIf $\tan A = \cot B$,prove that $A + B = 90^{\circ}$.
Easy
View SolutionProve the following identity,where the angle involved is an acute angle for which the expression is defined:
$\sqrt{\frac{1+\sin A}{1-\sin A}} = \sec A + \tan A$
$\sqrt{\frac{1+\sin A}{1-\sin A}} = \sec A + \tan A$
Medium
View SolutionExpress $\cot 85^{\circ}+\cos 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$.
Easy
View SolutionGiven $\tan A = \frac{4}{3},$ find the other trigonometric ratios of the $\angle A$.
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo