将f(x)=cos2x/cos(π/4+x)化成标准三角函数
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![将f(x)=cos2x/cos(π/4+x)化成标准三角函数](/uploads/image/z/4332933-45-3.jpg?t=%E5%B0%86f%28x%29%3Dcos2x%2Fcos%28%CF%80%2F4%2Bx%29%E5%8C%96%E6%88%90%E6%A0%87%E5%87%86%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0)
将f(x)=cos2x/cos(π/4+x)化成标准三角函数
将f(x)=cos2x/cos(π/4+x)化成标准三角函数
将f(x)=cos2x/cos(π/4+x)化成标准三角函数
f(x)=cos2x/cos(π/4+x)
=(cos²x-sin²x)/(√2/2cosx-√2/2sinx)
=(cosx+sinx)(cosx-sinx)/[√2/2(cosx-sinx)]
=√2(cosx+sinx)
=2(√2/2cosx+√2/2sinx)
=2sin(x+π/4)