(B) Given,$\tan A + \tan B = x$ and $\cot A + \cot B = y$. Since $\cot A + \cot B = \frac{1}{\tan A} + \frac{1}{\tan B} = \frac{\tan A + \tan B}{\tan

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) Given,$\tan A + \tan B = x$ and $\cot A + \cot B = y$. Since $\cot A + \cot B = \frac{1}{\tan A} + \frac{1}{\tan B} = \frac{\tan A + \tan B}{\tan A \tan B} = y$. Substituting $\tan A + \tan B = x$,we get $\frac{x}{\tan A \tan B} = y$,which implies $\tan A \tan B = \frac{x}{y}$. Now,using the formula $\tan (A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$,$\tan (A + B) = \frac{x}{1 - \frac{x}{y}} = \frac{x}{\frac{y - x}{y}} = \frac{xy}{y - x}$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Trigonometrical ratios of sum and difference of two and three angles

Medium

If $\tan A + \tan B = x$ and $\cot A + \cot B = y$,then $\tan (A + B) =$

AP EAMCET 2023 All AP EAMCET

A
$\frac{xy}{x-y}$
B
$\frac{xy}{y-x}$
C
$\frac{xy}{x+y}$
D
$\frac{x-y}{xy}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Ratios, Functions and Identities

Subtopic

Trigonometrical ratios of sum and difference of two and three angles

Previous Year

AP EAMCET 2023 Paper All AP EAMCET years →

The value of $\cos 12^\circ + \cos 84^\circ + \cos 156^\circ + \cos 132^\circ$ is

Easy

View Solution

$\tan 20^\circ + \tan 40^\circ + \sqrt{3} \tan 20^\circ \tan 40^\circ = $

Medium

View Solution

If $\sin \theta = \frac{12}{13}$ where $0 < \theta < \frac{\pi}{2}$ and $\cos \phi = -\frac{3}{5}$ where $\pi < \phi < \frac{3\pi}{2}$,then $\sin(\theta + \phi)$ is equal to:

Easy

View Solution

If $A=35^{\circ}, B=15^{\circ}$ and $C=40^{\circ}$,then $\tan A \cdot \tan B+\tan B \cdot \tan C+\tan C \cdot \tan A$ is equal to

MediumTS EAMCET 2008

View Solution

If two acute angles $A$ and $B$ are such that $A \neq B$ and $\frac{x}{y}=\frac{\cos A}{\cos B}$,then $\frac{x \tan A-y \tan B}{x+y}=$

DifficultAP EAMCET 2023

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If $\tan A + \tan B = x$ and $\cot A + \cot B = y$,then $\tan (A + B) =$

Similar Questions

The value of $\cos 12^\circ + \cos 84^\circ + \cos 156^\circ + \cos 132^\circ$ is

$\tan 20^\circ + \tan 40^\circ + \sqrt{3} \tan 20^\circ \tan 40^\circ = $

If $\sin \theta = \frac{12}{13}$ where $0 < \theta < \frac{\pi}{2}$ and $\cos \phi = -\frac{3}{5}$ where $\pi < \phi < \frac{3\pi}{2}$,then $\sin(\theta + \phi)$ is equal to:

If $A=35^{\circ}, B=15^{\circ}$ and $C=40^{\circ}$,then $\tan A \cdot \tan B+\tan B \cdot \tan C+\tan C \cdot \tan A$ is equal to

If two acute angles $A$ and $B$ are such that $A \neq B$ and $\frac{x}{y}=\frac{\cos A}{\cos B}$,then $\frac{x \tan A-y \tan B}{x+y}=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module