作业帮已知函数f(x)=2sin²(x+π/4)-根号3cos2x,x∈[π/4,π/2].设x=α时f(x)取到最大值.(1)求f(x)的最大值及α的值;(2)在△ABC中,角A,B,C所对的边分别为a,b,c,A=α-π/12,且sinBsinC=sin²A,求b-c的值.
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![已知函数f(x)=2sin²(x+π/4)-根号3cos2x,x∈[π/4,π/2].设x=α时f(x)取到最大值.(1)求f(x)的最大值及α的值;(2)在△ABC中,角A,B,C所对的边分别为a,b,c,A=α-π/12,且sinBsinC=sin²A,求b-c的值.](/uploads/image/z/1985499-27-9.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D2sin%26%23178%3B%28x%2B%CF%80%2F4%29-%E6%A0%B9%E5%8F%B73cos2x%2Cx%E2%88%88%5B%CF%80%2F4%2C%CF%80%2F2%5D.%E8%AE%BEx%3D%CE%B1%E6%97%B6f%28x%29%E5%8F%96%E5%88%B0%E6%9C%80%E5%A4%A7%E5%80%BC.%281%29%E6%B1%82f%28x%29%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E5%8F%8A%CE%B1%E7%9A%84%E5%80%BC%3B%282%29%E5%9C%A8%E2%96%B3ABC%E4%B8%AD%2C%E8%A7%92A%2CB%2CC%E6%89%80%E5%AF%B9%E7%9A%84%E8%BE%B9%E5%88%86%E5%88%AB%E4%B8%BAa%2Cb%2Cc%2CA%3D%CE%B1-%CF%80%2F12%2C%E4%B8%94sinBsinC%3Dsin%26%23178%3BA%2C%E6%B1%82b-c%E7%9A%84%E5%80%BC.)
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已知函数f(x)=2sin²(x+π/4)-根号3cos2x,x∈[π/4,π/2].设x=α时f(x)取到最大值.(1)求f(x)的最大值及α的值;(2)在△ABC中,角A,B,C所对的边分别为a,b,c,A=α-π/12,且sinBsinC=sin²A,求b-c的值.
已知函数f(x)=2sin²(x+π/4)-根号3cos2x,x∈[π/4,π/2].设x=α时f(x)取到最大值.
(1)求f(x)的最大值及α的值;
(2)在△ABC中,角A,B,C所对的边分别为a,b,c,A=α-π/12,且sinBsinC=sin²A,求b-c的值.
已知函数f(x)=2sin²(x+π/4)-根号3cos2x,x∈[π/4,π/2].设x=α时f(x)取到最大值.(1)求f(x)的最大值及α的值;(2)在△ABC中,角A,B,C所对的边分别为a,b,c,A=α-π/12,且sinBsinC=sin²A,求b-c的值.
（1）f(x)=2sin²(x+π/4)-√3cos2x
=(sinx+cosx)²-√3cos2x
=1+sin2x-√3cos2x
=2(cosπ/3sin2x-sinπ/3cos2x)+1
=2sin(2x-π/3)+1
∴f(x)的最大值=3
此时2x-π/3=2kπ+π/2
即α=kπ+5π/12
（2）sinBsinC=sin²A
A=5π/12-π/12=π/3
sinBsinC=sin²A
bc=a²=b²+c²-2bccosπ/3
∴b²-2bc+c²=0→(b-c)²=0
∴b-c=0