Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

{\text }{ If } 3 \tan A=2 \tan B  then what is the value of tan (A+B) ? 

Option: 1

\frac{5 \sin 2A}{5 \cos 2A-1}


Option: 2

\frac{ \sin 2A}{ \cos 2A-1}


Option: 3

\frac{5 \sin 2A}{5 \cos 2A-4}


Option: 4

\frac{\frac{5}{2} \sin 2A}{5 \cos 2A-1}


Answers (1)

best_answer

Sum/Difference into Product -

Sum/Difference into Product-

 

\\1.\;\;\sin \alpha+\sin \beta=2 \sin \left(\frac{\alpha+\beta}{2}\right) \cos \left(\frac{\alpha-\beta}{2}\right)\\\\2.\;\;\sin \alpha-\sin \beta=2 \sin \left(\frac{\alpha-\beta}{2}\right) \cos \left(\frac{\alpha+\beta}{2}\right)\\\\3.\;\;\cos \alpha-\cos \beta=-2 \sin \left(\frac{\alpha+\beta}{2}\right) \sin \left(\frac{\alpha-\beta}{2}\right)\\\\4.\;\;\cos \alpha+\cos \beta=2 \cos \left(\frac{\alpha+\beta}{2}\right) \cos \left(\frac{\alpha-\beta}{2}\right)

-

Given\ 3 \tan A = 2\tan B\\ \tan (A+B)= \frac{\tan A+\tan B}{1-\tan A \tan B}\\ = \frac{\tan A+\frac{3}{2} \tan A}{1-\tan A\ \frac{3}{2}\tan A}\\ =\frac{ \frac{5}{2}\ \tan A}{1-\frac{3}{2} \tan^2 A}\\ =\frac{5 \sin A \cos A}{2 \cos^2 A-3\sin^2 A}\\ =\frac{\frac{5}{2} \sin 2A}{(1+ \cos 2A)- \frac{3}{2}(1-cos 2A)} \\ =\frac{5 \sin 2A}{5 \cos 2A-1}

Posted by

Ajit Kumar Dubey

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

In JEE Main 2025 April 3 shift 2, chemistry takes U-turn to be tougher than physics, mathematics
anam-khan

JEE Main 2025 April 3 Exam Analysis 2025: Shift 1 paper easy to moderate; chemistry section ‘easiest’
anam-khan

JEE Mains 2025 admit card out for April 7, 8, 9 exams; download on jeemain.nta.nic.in

Latest Question