Grade 11Trigonometry

tanx +tan4x +tan7x=tanxtan4xtan7x

pawan punasya

14 Years agoGrade 11

2 Answers

Akshith Yeso

14 Years ago

Given tanx+tan4x+tan7x=tanxtan4tan7x

We know that tan(a+b+c)=tana+tanb+tanc-tanatanbtanc/1-(tanatanb+tanbtanc+tanctana)

If a+b+c is n(pie),n belongs to N then tan(a+b+c)=0

=> tana+tanb+tanc-tanatanbtanc=0

=>tana+tanb+tanc=tanatanbtanc

it is same as the given question,

Hence , x+4x+7x=n(pie)

=>12x=n(pie)

=> x=n(pie)/12

ruchi yadav

12 Years ago

Given tanx+tan4x+tan7x=tanxtan4tan7x

We know that tan(a+b+c)=tana+tanb+tanc-tanatanbtanc/1-(tanatanb+tanbtanc+tanctana)

 If a+b+c is n(pie),n belongs to N then tan(a+b+c)=0

 => tana+tanb+tanc-tanatanbtanc=0

 =>tana+tanb+tanc=tanatanbtanc

 it is same as the given question,

 Hence , x+4x+7x=n(pie)

 =>12x=n(pie)

                =>x=n(pie)/12 

Thank You
Ruchi
Askiitians Faculty