f(x)=2sin((pai\4)+x\2)乘以cos( (pai\4)+x\2 )+a sinx (x属于R) 的图像关于直线XX=pai\8对称,则g(x)=a sin( ( a+1)x )的最小正周期是?
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![f(x)=2sin((pai\4)+x\2)乘以cos( (pai\4)+x\2 )+a sinx (x属于R) 的图像关于直线XX=pai\8对称,则g(x)=a sin( ( a+1)x )的最小正周期是?](/uploads/image/z/6875745-33-5.jpg?t=f%28x%29%3D2sin%28%28pai%5C4%29%2Bx%5C2%29%E4%B9%98%E4%BB%A5cos%28+%28pai%5C4%29%2Bx%5C2+%29%2Ba+sinx+%28x%E5%B1%9E%E4%BA%8ER%29+%E7%9A%84%E5%9B%BE%E5%83%8F%E5%85%B3%E4%BA%8E%E7%9B%B4%E7%BA%BFXX%3Dpai%5C8%E5%AF%B9%E7%A7%B0%2C%E5%88%99g%28x%29%3Da+sin%28+%28+a%2B1%29x+%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E6%98%AF%3F)
f(x)=2sin((pai\4)+x\2)乘以cos( (pai\4)+x\2 )+a sinx (x属于R) 的图像关于直线XX=pai\8对称,则g(x)=a sin( ( a+1)x )的最小正周期是?
f(x)=2sin((pai\4)+x\2)乘以cos( (pai\4)+x\2 )+a sinx (x属于R) 的图像关于直线X
X=pai\8对称,则g(x)=a sin( ( a+1)x )的最小正周期是?
f(x)=2sin((pai\4)+x\2)乘以cos( (pai\4)+x\2 )+a sinx (x属于R) 的图像关于直线XX=pai\8对称,则g(x)=a sin( ( a+1)x )的最小正周期是?
f(x)=sin(π/2+x)+asinx
=cosx+asinx,
它的图像关于直线x=π/8对称,
∴f(π/4-x)=f(x),
即cos(π/4-x)+asin(π/4-x)=cosx+asinx,
(cosx+sinx+acosx-asinx)/√2=cosx+asinx,
∴a[cosx-(1+√2)sinx]=(√2-1)cosx-sinx,
∴a=√2-1,
∴g(x)=(√2-1)sin(x√2)最小正周期=π√2.