chứng minh

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lan_phuong_000

$sin^2(a+b) - sin^2a - sin^2b = 2.sina.sinb.cos(a+b)$
$ VT = sin^2(a+b) - sin^2a - sin^2b$
$= (sina.cosb + cosa.sinb)^2 - sin^2a - sin^2b$
$= sin^2a.cos^2b + 2.sina.sinb.cosa.cosb + cos^2a.sin^2b - sin^2a - sin^2b$
$= sin^2a.cos^2b - sin^2a + cos^2a.sin^2b - sin^2b + 2.sina.sinb.cosa.cosb$
$= sin^2a.(cos^2b -1) + sin^2b.(cos^2a -1) + 2.sina.sinb.cosa.cosb$
$= -sin^2a.sin^2b - sin^2b.sin^2a + 2.sina.sinb.cosa.cosb$
$= 2sina.sinb(cosa.cosb - sina.sinb)$
$= 2.sina.sinb.cos(a + b) = VP (dpcm)$
 
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