已知函数f(x)=sinx+sin(x+pi/2) 求F(X)最小正周期

f(x)=sinx+sin(x+π/2)
=sinx+cosx
=√2sin(x+π/4)
1.T=2π
2.f(x)max=√2 ,f(x)min=-√2
3.f(a)=sina+cosa=3/4
(sina)^2+(cosa)^2+2sinacoaa=9/16
1+sin2a=9/16
所以sin2a=-7/16