Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

i am trying to solve following problems and please guys help me suppose that,there is given following equation $[f(x)]^2-[f(y)]^2$=$f(x+y) \cdot f(x-y)$ there was said that,it requires some knowledge of calculus,first of all i factor this equation as $(f(x)+f(y)) \cdot (f(x)-f(y))$=$f(x+y)\cdot f(x-y)$ so it means that

1.$f(x)+f(y)=f(x+y)$ 2.$f(x)-f(y)=f(x-y)$ so it means that $f(x)=a \cdot x$ right yes?where does it requires calculus?range of x,y are all real numbers

share|improve this question
    
$f \ast f \neq |f|^2$ –  plusepsilon.de Apr 13 '12 at 13:02
    
You could use "\cdot" instead of "$*$" –  Beni Bogosel Apr 13 '12 at 15:25
    
If two products are equal it doesn't mean the terms are equal. Your conclusions 1) and 2) are not right... –  N. S. Apr 19 '12 at 12:14

1 Answer 1

up vote 6 down vote accepted

That is called the Sine Functional Equation; for the beginning you may check this page. It mentions that $f(x)=kx$ satisfies this equation. And of course $\sin^2(x)-\sin^2(y)=\sin(x+y)\cdot \sin(x-y)$

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.