sin²20°+sin²25°＋√2sin20°sin25°

sin²20°+sin²25°＋√2sin20°sin25°
sin²20°+sin²25°＋√2sin20°sin25°

sin²20°+sin²25°＋√2sin20°sin25°
sin²20 + sin²25 + √2sin20sin25
= (1 - cos40)/2 + (1 - cos50)/2 + (√2)(1/2)[cos(20 - 25) - cos(20 + 25)]
= 1 - (1/2)(cos40 + cos50) + (√2/2)(- cos5 - cos45)
= 1 - (1/2)(2)cos[(40 + 50)/2]cos[(40 - 50)/2] - (√2/2)cos5 - (√2/2)(√2/2)
= 1 - cos45cos5 + (√2/2)cos5 - 1/2
= 1/2 - (√2/2)cos5 + (√2/2)cos5
= 1/2
公式：
sin²θ = (1 - cos2θ)/2
sinxsiny = (1/2)[cos(x - y) - cos(x + y)]
cosx + cosy = 2cos[(x + y)/2]cos[(x - y)/2]