y=cos(a+π/4)+sin2a化简详解

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y=cos(a+π/4)+sin2a化简详解
y=cos(a+π/4)+sin2a化简详解

y=cos(a+π/4)+sin2a化简详解
y=cos(a+π/4)+sin2a
=√2/2(cosa-sina)+sin2a
令cosa-sina=t,则两边平方得1-sin2a=t²
所以y=√2t/2+1-t²

y=cos(a+π/4)-cos(2a+π/2)
=cos(a+π/4)-cos[2(a+π/4)]
=cos(a+π/4)-1+2cos²(a+π/4)
=2cos²(a+π/4)+cos(a+π/4)-1
若设:cos(a+π/4)=x
则:y=2x²+x-1 【转化为闭区间上的二次函数】