show that cos² na-cos²ma=sin(m+n)asin(m-n)a
Plx help me to do it,
L.H.S.
(cosna-cosma)(cosna+cosma)
=(-2)sin(na+ma/2)sin(na-ma/2)x(2)cos(ma+na/2)cos(na-na/2)
=(-2)sin(na+ma/2)cos(ma+na/2)x(2)sin(na-ma/2)cos(na-na/2)
trgo (2)
2007-03-19 7:56 pm
回答 (1)
2007-03-19 8:22 pm
✔ 最佳答案
R.H.S.sin(m+n)asin(m-n)a = sin(ma+na)sin(ma-na)
Let x=ma & y=na
= (sinxcosy+cosxsiny)(sinxcosy-cosxsiny)
= sin²xcos²y+cosxcosysinxsiny-cosxcosysinxsiny-cos²xsin²y
= sin²xcos²y-cos²xsin²y
= (1-cos²x)cos²y-cos²x(1-cos²y)
= cos²y-cos²xcos²y-cos²x+cos²xcos²y
= cos²y-cos²x
= cos²na-cos²ma=L.H.S.
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