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**RauLiTo****Member**- From: Bahrain
- Registered: 2006-01-11
- Posts: 142

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)*

ImPo$$!BLe = NoTH!nG

Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,094

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....

Character is who you are when no one is looking.

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**kempos****Member**- Registered: 2006-01-07
- Posts: 77

maybe this will help

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