高一三角函数化简 sin^2(x-30)+sin^2(x+30)-sin^2(x)

问题描述:

高一三角函数化简 sin^2(x-30)+sin^2(x+30)-sin^2(x)
1个回答 分类:数学 2014-11-29

问题解答:

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sin^2(x-30)+sin^2(x+30)-sin^2(x)
=(1-cos(2x-60))/2+(1-cos(2x+60))/2-sin^2x
=1-1/2[cos(2x-60)+cos(2x+60)]-sin^2x
=-1/2[cos2xcos60+sin2xsin60+cos2xcos60-sin2xsin60]+cos^2
=-1/2[2×1\2cos2x]+cos^2
=cos^2-1/2cos2x
=(1+cos2x)\2-1/2cos2x
=1/2 一般三角函数化简多是求值的大多得的是确切的数字
 
 
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