高一数学题,求高手,在线等,急~!

高一数学题,求高手,在线等,急~!
1、求sin3π/8cosπ/8+cos3π/8sinπ/8的值
2、将下列各式表示成一个角的正弦:
(1)sin3π/7cos2π/5-cos(-3π/7)sin(-2π/5)
(2)cosπ/4sin[α+(π/4)]-sin[(π/4)-α]sinπ/4
shelley_99 1年前 已收到2个回答 举报

hq123 幼苗

共回答了12个问题采纳率:100% 举报

①sin3π/8*cosπ/8+cos3π/8*sinπ/8=sin(3π/8+π/8)=sinπ/2=1
②原式=sin(3π/7)*cos(2π/5)+cos(3π/7)*sin(2π/5) (化为同角)
=sin(3π/7+2π/5) (两角和的正弦公式的逆运用)
=sin(29π/35)=sin(6π/35)(互补两角的正弦相等)
原式=sin[α+(π/4)]cosπ/4-cos[(π/4)+α]sinπ/4
=sin[α+(π/4)-(π/4)]=sinα

1年前

6

Girlieshow 幼苗

共回答了258个问题 举报

1.原式=sin(3π/8+π/8)=sin(π/2)=1
2.(1).原式=sin3π/7cos2π/5+cos3π/7sin2π/5=sin(3π/7+2π/5)=sin(29π/35)
(2)原式=cosπ/4sin(α+π/4)+cos[π/2-(π/4-α)]sinπ/4=cosπ/4sin(α+π/4)-sinπ/4cos(α+π/4)=sin(α+π/4-π/4)=sinα
祝你好运~_~

1年前

0
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