If Tan X Tan 2x Tan 7x = Tan X+ Tan 2x+ Tan 7x, Then X - EduRev

EduRev

• Home
• Explore Courses
• Signup
• Pricing Plans
• EduRev Store
• View all Class 11 Docs
• View all Class 11 Videos
• View all Class 11 Tests
• EduRev Infinity
• View Analysis
• Raise a Demand

Less EduRev Explore Exams Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for FreeSign in Open App Class 11 Exam > Class 11 Questions > If tan x tan 2x tan 7x = tan x+ tan 2x+ tan 7... Start Learning for Free If tan x tan 2x tan 7x = tan x+ tan 2x+ tan 7x, then x=?

Clear all your Class 11 doubts with EduRev Join for Free

Join for Free

Verified AnswerIf tan x tan 2x tan 7x = tan x+ tan 2x+ tan 7x, then x=?Tan x + tan 2x + tan 3x - tan x tan 2x tan 3x = 0 tan x + tan 2x + tan 3x ( 1 - tan x tan 2x ) = 0 tan x + tan 2x = - tan 3x ( 1 - tan x tan 2x ) ( tan x + tan 2x )/ ( 1 - tan x tan 2x ) = - tan 3x tan 3x = - tan 3x 2 tan 3x = 0 tan 3x = 0 3x = 2kpi where k = 0, 1,2,3,4,5,... x = 2 k pi/3 where k = 0 , 1, 2 ,3 , 4 , 5 , 6.This question is part of UPSC exam. View all Class 11 coursesMost Upvoted AnswerIf tan x tan 2x tan 7x = tan x+ tan 2x+ tan 7x, then x=?Solution:To solve the given equation, we will use the trigonometric identity:tan A tan B = tan (A + B) - tan (A - B)Let's rewrite the given equation using this identity:tan x tan 2x tan 7x = tan x tan 2x tan 7xNow, we can apply the identity to both sides of the equation:tan (x + 2x) - tan (x - 2x) = tan (x + 2x) - tan (x - 2x)Simplifying the equation further:tan 3x - tan (-x) = tan 3x - tan (-x)Since tan (-x) = -tan x, we can rewrite the equation as:tan 3x + tan x = tan 3x + tan xNow, let's combine like terms on both sides of the equation:2tan 3x = 2tan 3xDividing both sides of the equation by 2, we get:tan 3x = tan 3xThis equation holds true for all values of x. Therefore, there are infinitely many solutions for x.Explanation:The given trigonometric equation, tan x tan 2x tan 7x = tan x tan 2x tan 7x, can be simplified using the trigonometric identity tan A tan B = tan (A + B) - tan (A - B). By applying this identity, we obtain the equation tan 3x - tan (-x) = tan 3x - tan (-x). Since tan (-x) = -tan x, we can rewrite the equation as tan 3x + tan x = tan 3x + tan x. By combining like terms on both sides, we arrive at the equation 2tan 3x = 2tan 3x. Dividing both sides by 2, we get tan 3x = tan 3x. This equation holds true for all values of x, which means there are infinitely many solutions for x.Answered by Prof. Tarun Kaushik · View profileShare your Answer

Explore Courses for Class 11 exam

Top Courses for Class 11View all

Mathematics (Maths) Class 11

Chemistry Class 11

English Snapshot Class 11

Business Studies CUET UG Mock Test Series 2026

CUET Science Subjects Mock Tests 2026

Top Courses for Class 11

View all Question Description If tan x tan 2x tan 7x = tan x+ tan 2x+ tan 7x, then x=? for Class 11 2026 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If tan x tan 2x tan 7x = tan x+ tan 2x+ tan 7x, then x=? covers all topics & solutions for Class 11 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If tan x tan 2x tan 7x = tan x+ tan 2x+ tan 7x, then x=?.Solutions for If tan x tan 2x tan 7x = tan x+ tan 2x+ tan 7x, then x=? in English & in Hindi are available as part of our courses for Class 11. Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.Here you can find the meaning of If tan x tan 2x tan 7x = tan x+ tan 2x+ tan 7x, then x=? defined & explained in the simplest way possible. Besides giving the explanation of If tan x tan 2x tan 7x = tan x+ tan 2x+ tan 7x, then x=?, a detailed solution for If tan x tan 2x tan 7x = tan x+ tan 2x+ tan 7x, then x=? has been provided alongside types of If tan x tan 2x tan 7x = tan x+ tan 2x+ tan 7x, then x=? theory, EduRev gives you an ample number of questions to practice If tan x tan 2x tan 7x = tan x+ tan 2x+ tan 7x, then x=? tests, examples and also practice Class 11 tests.

Explore Courses for Class 11 exam

Top Courses for Class 11

Explore CoursesJoin the Discussion on the App for FREE

Related Content

Signup for Free!Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.Start learning for Free10M+ students study on EduRev×

Share your doubts

SubmitxFor Your Perfect Score in Class 11The Best you need at One PlaceStart Your Infinity Experience

Home

Courses

Infinity

Get App

View answers on AppView all answers and join this discussion on the EduRev AppView in AppNot Now × Signup to see your scores go up within 7 days!Access 1000+ FREE Docs, Videos and TestsContinue with GoogleTakes less than 10 seconds to signup