化简sin^2(a)*sin^2(b)+cos^2(a)*cos^2(b)-1/2cos2a*cos2b
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化简sin^2(a)*sin^2(b)+cos^2(a)*cos^2(b)-1/2cos2a*cos2b
利用公式把变量的形式化简得越少越好
(sina)^2*(sinb)^2+(cosa)^2*(cosb)^2-1/2cos2a*cos2b
=(1-(cosa)^2)(1-(cosb)^2)+(cosa)^2*(cosb)^2-1/2(2(cosa)^2-1)(2(cosb)^2-1)
=1+(cosacosb)^2-(cosa)^2-(cosb)^2+(cosacosb)^2-1/2[1-2(cosa)^2-2(cosb)^2+4(cosacosb)^2]
=1+2(cosacosb)^2-(cosa)^2-(cosb)^2-1/2+(cosa)^2+(cosb)^2-2(cosacosb)^2
=1-1/2
=1/2
sin^2(a)*sin^2(b)+cos^2(a)*cos^2(b)-1/2cos2a*cos2b
=sin^2(a)*sin^2(b)+cos^2(a)*cos^2(b)-1/2(cos^2(a)-sin^2(a))(cos^2(b)-sin^2(b))
=1/2(sin^2(a)*sin^2(b)+cos^2(a)*cos^2(b)+cos^2(a)*sin^2(b)+sin^2(a)*cos^2(b))
=1/2(sin^2(a)*(sin^2(b)+cos^2(b))+1/2(cos^2(a)*(cos^2(b)+sin^2(b))
=1/2+sin^2(a)+1/2cos^2(a)
=1/2
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