Question

若sin(a+π/4)=a，则cos(a-π/4）=多少

Answer 1

cos(a-π/4）=cos（π/4-a）=sin（π/2-（π/4-a））=cos（a+π/4）
sin(a+π/4)=a
所以cos（a+π/4）=±根号（1-a²）

也可以
cos(a-π/4）=sin(π/2-(a-π/4))
=sin(3π/4-a)=sin(π-（3π/4-a）)=sin(a+π/4)=a

Answer 2

解析：∵sin(α+π/4)=√2/2*（sinα+cosα)=a
又cos(α-π/4）=√2/2*（sinα+cosα)，
∴cos(α-π/4）=a,
题目应该α，不是a,就更好了。

Answer 3

因为(a-π/4)-(a+π/4)=-π/2
所以cos(a-π/4）=sin(a+π/4)=a

Answer 4

cos(a-π/4）=sin(π/2-(a-π/4))
=sin(3π/4-a)=-sin(-π/4-a)=sin(a+π/4)=a

Answer 5

a