Math Is Fun Forum

RauLiTo

Member

From: Bahrain

Registered: 2006-01-11

Posts: 142

trigonometry

A and B are two acute angles. Prove that if
sin² (A) + sin² (B) = sin( A + B ), then
A + B  = 180/2.

waiting for your help

Last edited by RauLiTo (2006-05-08 23:22:46)

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ImPo$$!BLe = NoTH!nG
Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,390

Re: trigonometry

RHS=sin(A+B)=sinAcosB+cosAsinB
If A+B=90, B=90-A, A=90-B;
cosB=sin(90-B)=sinA
sinB=cos(90-B)=cosA
Therefore RHS=sin²A+cos²A=1
LHS=sin²A+sin²B, since sinB=cosA,
sin²B=cos²A,
therefore, LHS=1=RHS.
We find the equation is true when A+B=90 degrees or
(A+B)/2=180. Shall try to prove later....

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kempos

Member

Registered: 2006-01-07

Posts: 77

Re: trigonometry

maybe this will help