求证:cos²(π/4+a/2)-sin²(π/4+a/2)=cos(π/2+a)
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![求证:cos²(π/4+a/2)-sin²(π/4+a/2)=cos(π/2+a)](/uploads/image/z/2522657-65-7.jpg?t=%E6%B1%82%E8%AF%81%3Acos%26%23178%3B%28%CF%80%2F4%2Ba%2F2%29-sin%26%23178%3B%28%CF%80%2F4%2Ba%2F2%29%3Dcos%28%CF%80%2F2%2Ba%29)
求证:cos²(π/4+a/2)-sin²(π/4+a/2)=cos(π/2+a)
求证:cos²(π/4+a/2)-sin²(π/4+a/2)=cos(π/2+a)
求证:cos²(π/4+a/2)-sin²(π/4+a/2)=cos(π/2+a)
左=cos²(π/4+a/2)-sin²(π/4+a/2)
=cos[2(π/4+a/2)]
=cos(π/2+a)=右
倍角公式:
cos2a=cos²a-sin²a
由公式cos²x-sin²x=cos(2x)即得
由半角公式
cos²(π/4+a/2)-sin²(π/4+a/2)=cos[2(π/4+a/2)]=cos(π/2+a)