已知sin(x+π⼀6)的 =1⼀4,求sin(7π⼀6 +x)+cos(5π⼀6 -x)的平方的值

答案是11⼀16
2025-02-24 00:28:53
推荐回答(1个)
回答1:

sin(x+π/6)的 =1/4
sin(7π/6 +x)+ [cos(5π/6 -x)]^2
=sin(π+π/6 +x)+[cos[π-(π/6+x)]^2
=-sin(x+π/6) + [cos(x+π/6)]^2
=-sin(x+π/6) + {[1-[sin(x+π/6)]^2}
=-1/4+[1-(1/4)^2]
=-1/4+1-1/16
=11/16