已知sin(x+π/6)=1/4,求sin(7π/6+x)+cos^2(5π/6-x)

因为sin(x+π/6)=1/4,
所以sin(7π/6+x)=sin(π+π/6+x)=-sin(x+π/6)=-1/4,
cos^(5π/6-x)=cos^(π-(π/6+x))=cos^(x+π/6)=1-sin^(x+π/6)=1-/16=15/16.
sin(7π/6+x)+cos^2(5π/6-x)=-1/4+15/16=11/16

sin(x+7π/6)＝sin(x＋π/6＋π)＝－sin(x+π/6)＝－1/4
cos(11π/6-x)＝cos(2π－(x+π/6))＝cos(x+π/6)＝±√15/4
所以，sin(x+7π/6)+cos^2 (11π/6-x)＝－1/4＋15/16＝11/16