Class 11MathematicsTrigonometrical Ratios, Functions and IdentitiesMix Examples-Trigonometrical Ratios, Functions and Identities
Mediumसिद्ध कीजिए कि $\cot x \cot 2x - \cot 2x \cot 3x - \cot 3x \cot x = 1$ है।
(A) $L.H.S. = \cot x \cot 2x - \cot 2x \cot 3x - \cot 3x \cot x$
$= \cot x \cot 2x - \cot 3x(\cot 2x + \cot x)$
$= \cot x \cot 2x - \cot(2x + x)(\cot 2x + \cot x)$
$= \cot x \cot 2x - \left[ \frac{\cot 2x \cot x - 1}{\cot x + \cot 2x} \right](\cot 2x + \cot x)$
$\left[ \because \cot(A + B) = \frac{\cot A \cot B - 1}{\cot A + \cot B} \right]$
$= \cot x \cot 2x - (\cot 2x \cot x - 1) = 1 = R.H.S.$
$= \cot x \cot 2x - \cot 3x(\cot 2x + \cot x)$
$= \cot x \cot 2x - \cot(2x + x)(\cot 2x + \cot x)$
$= \cot x \cot 2x - \left[ \frac{\cot 2x \cot x - 1}{\cot x + \cot 2x} \right](\cot 2x + \cot x)$
$\left[ \because \cot(A + B) = \frac{\cot A \cot B - 1}{\cot A + \cot B} \right]$
$= \cot x \cot 2x - (\cot 2x \cot x - 1) = 1 = R.H.S.$
Explore More
Similar Questions
व्यंजक $2 \cos \frac{\pi}{13} \cos \frac{9\pi}{13} + \cos \frac{3\pi}{13} + \cos \frac{5\pi}{13}$ का मान क्या है?
Medium
View Solutionयदि $\theta$ तीसरे चतुर्थांश में है,तो $\sqrt{4 \sin ^4 \theta+\sin ^2 2 \theta}+4 \cos ^2\left(\frac{\pi}{4}-\frac{\theta}{2}\right)=$
यदि $\cosh x = \operatorname{cosec} \theta$ है,तो $\coth^2 \frac{x}{2} = $
DifficultAP EAMCET 2023
View Solution$\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}=$
यदि $\sec \theta + \tan \theta = p$ है,तो $\tan \theta$ का मान क्या होगा?
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