(B) Given $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3}$.We know that $\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} = \frac{\frac{1}{2}

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

(B) Given $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3}$.We know that $\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} = \frac{\frac{1}{2} + \frac{1}{3}}{1 - (\frac{1}{2} \times \frac{1}{3})} = \frac{\frac{5}{6}}{1 - \frac{1}{6}} = \frac{\frac{5}{6}}{\frac{5}{6}} = 1$.Since $\tan(A + B) = 1$,we have $A + B = 45^\circ$.Therefore,$2A = 90^\circ - 2B$.Taking cosine on both sides,$\cos 2A = \cos(90^\circ - 2B) = \sin 2B$.

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

Easy

If $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3}$,then $\cos 2A = $

A
$\sin B$
B
$\sin 2B$
C
$\sin 3B$
D
None of these

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

If $\frac{\sin(x+y)}{\sin(x-y)} = \frac{a+b}{a-b}$,then $\frac{\tan x}{\tan y} = $

EasyTS EAMCET 2021

View Solution

For $\theta \in \left(0, \frac{\pi}{2}\right)$,if $\tan 3\theta \cdot \tan 2\theta \cdot \tan \theta + \tan 2\theta + \tan \theta = 1$,then $\theta =$

MediumMHT CET 2020

View Solution

If $\sin A = -\frac{24}{25}$,$\cos B = \frac{15}{17}$,$A$ does not belong to the $4^{\text{th}}$ quadrant,and $B$ does not belong to the $1^{\text{st}}$ quadrant,then $(A+B)$ lies in which quadrant?

MediumTS EAMCET 2025

View Solution

The value of $\frac{\tan 70^o - \tan 20^o}{\tan 50^o} = $

Medium

View Solution

If $\cos (A-B)=3/5$ and $\tan A \tan B=2$,then which one of the following is true?

DifficultAP EAMCET 2007

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 $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3}$,then $\cos 2A = $

Similar Questions

If $\frac{\sin(x+y)}{\sin(x-y)} = \frac{a+b}{a-b}$,then $\frac{\tan x}{\tan y} = $

For $\theta \in \left(0, \frac{\pi}{2}\right)$,if $\tan 3\theta \cdot \tan 2\theta \cdot \tan \theta + \tan 2\theta + \tan \theta = 1$,then $\theta =$

If $\sin A = -\frac{24}{25}$,$\cos B = \frac{15}{17}$,$A$ does not belong to the $4^{\text{th}}$ quadrant,and $B$ does not belong to the $1^{\text{st}}$ quadrant,then $(A+B)$ lies in which quadrant?

The value of $\frac{\tan 70^o - \tan 20^o}{\tan 50^o} = $

If $\cos (A-B)=3/5$ and $\tan A \tan B=2$,then which one of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module