若sin(x+6/π)=1/3,求sin(7π/6+x)+cos2(5π/6-x)

题目

若sin(x+6/π)=1/3,求sin(7π/6+x)+cos2(5π/6-x)

答案

sin(7π/6+x)
=sin(π+π/6+x)
=-sin(π/6+x)
=-1/3
cos²(5π/6-x)
=1-sin²(5π/6-x)
=1-sin²[π-(5π/6-x)]
=1-sin²(π/6+x)
=8/9
所以原式=5/9