函数y=sin(x+π/4)+sin(π/4-x)的最大值为_______.

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函数y=sin(x+π/4)+sin(π/4-x)的最大值为_______.函数y=sin(x+π/4)+sin(π/4-x)的最大值为_______.函数y=sin(x+π/4)+sin(π/4-x

函数y=sin(x+π/4)+sin(π/4-x)的最大值为_______.
函数y=sin(x+π/4)+sin(π/4-x)的最大值为_______.

函数y=sin(x+π/4)+sin(π/4-x)的最大值为_______.
y=根号2/2*sinx+根号2/2*cosx+根号2/2*sinx-根号2/2*cosx=根号2*sinx
最大值为根号2

y=sin(x+π/4)+sin(π/4-x)
=2sin[(x+π/4+π/4-x)]/2cos(x+π/4-π/4+x)/2
=√2cosx
函数y=sin(x+π/4)+sin(π/4-x)的最大值为__√2

y=sin(x+π/4)+sin[π/2-(π/4+x)]
=sin(x+π/4)+cos(π/4+x)
=根号2*sin(x+π/4+π/4)
=根号2*cosx
最大值为根号2

用和差化积公式
y=sin(x+π/4)+sin(π/4-x)=2sinπ/4 cosx=√2 cosx
所以最大值为 √2