一道数学题:已知cos(x-π/4)=√2/10,x属于(π/2,3π/4)

问题描述:

一道数学题:已知cos(x-π/4)=√2/10,x属于(π/2,3π/4)
已知cos(x-π/4)=√2/10,x属于(π/2,3π/4).
(1)求sinx的值.
(2)求sin(2x+π/3)的值.

1:cos(x-π/4)=√2/2*(cosx+sinx)=√2/10
cosx+sinx=1/5
所以:sinx=4/5
2:cosx=-3/5
sin(2x+π/3)=1/2*sin2x+√3/2*cos2x
=1/2*2*sinx*cosx+√3/2*(1-2sinx*sinx)
=-12/25+9√3/50