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函数f(x)=1-2sin^2 (x+派/8)+2sin(x+派/8)cos(x+派/8)求详细化简

题目详情
函数f(x)=1-2sin^2 (x+派/8)+2sin(x+派/8)cos(x+派/8)求详细化简
▼优质解答
答案和解析
【cos2x=cos²x-sin²x
sin2x=2sinxcosx
sinx+cosx=√2sin(x+π/4) 】
f(x)=1-2sin^2 (x+派/8)+2sin(x+派/8)cos(x+派/8)
=sin²(x+π/8)+cos²(x+π/8)-2sin²(x+π/8)+2sin(x+π/8)cos(x+π/8)
=cos²(x+π/8)-sin²(x+π/8)+sin(2x+π/4)
=cos(2x+π/4)+sin(2x+π/4)
=√2sin(2x+π/4+π/4)
=√2sin(2x+π/2)
=√2sin[π/2-(-2x)]
=√2cos2x