(sinx-siny)/sin(x+y) = sin1/2(x-y)/sin1/2(x+y)

来源：学生作业帮编辑：搜搜做题作业网作业帮分类：数学作业时间：2024/07/29 17:38:01

(sinx-siny)/sin(x+y) = sin1/2(x-y)/sin1/2(x+y)
还有这个sec(π/4+α)sec(π/4-α)=2sec2α

sinx=sin[(x+y)/2]cos[(x-y)/2]+cos[(x+y)/2]sin[(x-y)/2]
siny=sin[(x+y)/2]cos[(x-y)/2]-cos[(x+y)/2]sin[(x-y)/2]
sinx-siny=2cos[(x+y)/2]sin[(x-y)/2]
sin(x+y)=2sin[(x+y)/2]cos[(x+y)/2]
所以(sinx-siny)/sin(x+y)=sin[(x-y)/2]/sin[(x+y)
sec(π/4+α)=1/cos(π/4+α)=1/(cosπ/4cosα-sinπ/4sinα)=(√2)/(cosα-sinα)
sec(π/4-α)=1/cos(π/4-α)=1/(cosπ/4cosα+sinπ/4sinα)=(√2)/(cosα+sinα)
所以sec(π/4+α)sec(π/4-α)=2/[(cosα)^2-(sinα)^2]=2/cos2α=2sec2α

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