已知cos(x)=-2√5/5,x∈(-π,0)求sin2x的值,求tan(2x+π/4)
问题描述：
已知cos(x)=-2√5/5,x∈(-π,0)求sin2x的值,求tan(2x+π/4)
答
cos(x)=-2√5/5,
x∈(-π,0)
所以
sinx=-√5/5
得
sin2x=2sinxcosx=4/5
cos2x=2cos²x-1=3/5
tan2x=4/3
得
tan(2x+π/4)
=(tan2x+tanπ/4)/(1-tan2xtanπ/4)
=(tan2x+1)/(1-tan2x)
=(4/3+1)/(1-4/3)
=-7