√1+2sin(π/2+α)cos(π/2-α)=___.
问题描述：
√1+2sin(π/2+α)cos(π/2-α)=___.
答
原式 = √[ (1 + 2sin(π/2+α)cos(π/2-α)) ]
= √(1 + 2cosα sinα)
= √[ (sin²α + cos²α) + 2cosα sinα ]
= √(sinα + cosα)²
= ∣sinα + cosα∣