x属于(0,π/2) (1+sinx)^1/2+(1-sinx)^1/2-(2+2cosx)^1/2=?
问题描述:
x属于(0,π/2) (1+sinx)^1/2+(1-sinx)^1/2-(2+2cosx)^1/2=?
答
因为 [sin(x/2)+cos(x/2)]²=1+2sin(x/2)cos(x/2)=1+sinx[sin(x/2)-cos(x/2)]²=1-2sin(x/2)cos(x/2)=1-sinx1+cosx=2cos²(x/2),且当 x/2∈(0,π/4)时,有sin(x/2)