Question

[cos(x/2-7π/8)]^2-[cos(x/2+7π/8)]^2可化简为什么啊~o(∩_∩)o 哈哈

Answer 1

根据平方差公式,得

[cos(x/2-7π/8)+cos(x/2+7π/8)][cos(x/2-7π/8)-cos(x/2+7π/8)]

分别用角和差的余弦公式展开,得

[2cos(x/2)cos(7π/8)][2sin(x/2)sin(7π/8)]=[2sin(x/2)cos(x/2)][2sin(7π/8)cos(7π/8)]

根据2倍角的正弦公式,得

sin(x)sin(7π/4)=[-(√2)/2]sin(x)

o(∩_∩)o 希望对你有所帮助!