cos(x-(4分之派))=10分之更号2 x属于(2分之派,4分之3派) 求sinx的值 求sin(2x+3分之派)的值 过程写下 谢~

写成这种形式,以便观察.
cos(x-π/4)=√2/10
则
cos(2x-π/2)=2·[cos(x-π/4)]^2-1
=2×2/100-1
=-24/25;
cos(2x-π/2)=sin 2x,
则sin 2x= -24/25.
于是
cos 2x=-√[1-(24/25)^2]
=-7/25.
则cos 2x=1-2·sin^2 x
即1-2·sin^2 x=-7/25
∴sinx=4/5.

sin(2x+3分之派)
=sin2x·cos(3分之派)+cos2x·sin(3分之派)
=(-24/25)·(1/2)+(-7/25)·(√3/2)
= -12/25 - (7√3) /50.