[Toan 10] Luong giac

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gt\Leftrightarrow sin(a+b)=-sinb.cosb
\Leftrightarrow 2sin(a+b)+sin2b=0
cần chứng minh:
\Leftrightarrow cos^3b.sina+sin^3b.cosa=sina.cosa
\Leftrightarrow (1-sin^2b)cosb.sina + (1-cos^2b).sinb.cosa=cosa.sina
\Leftrightarrow sina.cosb+sinb.cosa-sinb.cosbcos(a-b)=sina.cosa
\Leftrightarrow 2sin(a+b)-sin2b.cos(a-b)-sin2a=0
\Leftrightarrow sin2b+sin2a+sin2b.cos(a-b)=0
\Leftrightarrow 2sin(a+b).cos(a-b)+sin2b.cos(a-b)=0
\Leftrightarrow cos(a-b).(2.sin(a+b)+sin2b)=0 ( đúng đó gt cho 2sin(a+b)+sin2b=0)
\Rightarrow đpcm
 
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