若cos(派/4+x)=3/5,17派/12
问题描述：
若cos(派/4+x)=3/5,17派/12
答
π/4+x的范围是5π/3根据cos（π/4+x）=3/5
得出sin（π/4+x）=－4/5
sinx+cosx=√2sin(π/4+x）=－4√2/5
（sinx+cosx）^2=32/25 所以2sinxcosx=（sinx+cosx）^2－1=7/25
cosx－sinx=√2cos(π/4+x）=3√2/5
(sin2x+2sin^2x)/(1-tgx)
=( 2sinxcosx+2sin^2x)/(1-sinx/cosx)
=2sinx(cosx+sinx)/ (1-sinx/cosx)
=2sinxcosx(cosx+sinx)/(cosx-sinx)
=-28/75
答
17π/12＜x＜7π/4,得5π/3＜x+π/4＜2π cos(x-π/4)=cos[(x+π/4)-π/2]=sin(x+π/4)=-√[1-cos²(x+π/4)]=-√[1-(3/5)²]=-4/5 sin(2x)=-cos(2x+π/2)=-cos[2(x+π/4)]=1-2cos²(x+π/4)=1-2•...