已知函数f(x)=sin(2x+π/3)-cos(2x+π/6)+2cos平方x,求f(π/8)的值

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已知函数f(x)=sin(2x+π/3)-cos(2x+π/6)+2cos平方x,求f(π/8)的值已知函数f(x)=sin(2x+π/3)-cos(2x+π/6)+2cos平方x,求f(π/8)的值

已知函数f(x)=sin(2x+π/3)-cos(2x+π/6)+2cos平方x,求f(π/8)的值
已知函数f(x)=sin(2x+π/3)-cos(2x+π/6)+2cos平方x,求f(π/8)的值

已知函数f(x)=sin(2x+π/3)-cos(2x+π/6)+2cos平方x,求f(π/8)的值
f(x)=sin(2x+π/3)-cos(2x+π/6)+2cos²x
f (π/8)=sin7π/12-cos5π/12+2cos²π/8
=sin5π/12-cos5π/12+1+cosπ/4
=√2sin(5π/12-π/4)+1+√2/2
=√2sinπ/6+1+√2/2
=√2/2+1+√2/2
=√2+1 （根号2+1）
答：f(π/8)的值为√2+1,即根号2+1

ƒ(x) = sin(2x + π/3) - cos(2x + π/6) + 2cos²x
ƒ(π/8) = sin(π/4 + π/3) - cos(π/4 + π/6) + 2cos²(π/8)
= sin(π/4)cos(π/3) + cos(π/4)sin(π/3) - [cos(π/4)cos(π/6) - sin(π/4)sin...

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ƒ(x) = sin(2x + π/3) - cos(2x + π/6) + 2cos²x
ƒ(π/8) = sin(π/4 + π/3) - cos(π/4 + π/6) + 2cos²(π/8)
= sin(π/4)cos(π/3) + cos(π/4)sin(π/3) - [cos(π/4)cos(π/6) - sin(π/4)sin(π/6)] + 1 + cos(π/4)
= √2/2 · 1/2 + √2/2 · √3/2 - √2/2 · √3/2 + √2/2 · 1/2 + 1 + √2/2
= √2/4 + √6/4 - √6/4 + √2/4 + √2/2 + 1
= √2/2 + √2/2 + 1
= √2 + 1

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