已知sin(x+6/π)=4/1,求sin(6/5π-x)+sin^2(3/π-x)的值

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首先稍微更正下 一般2分之1 在电脑中是用1/2 表示的
(x+π/6)+(5π/6-x)=π,(x+π/6)+(π/3-x)=π/2
根据诱导公式：
sin(5π/6-x)=sin[π-(x+π/6)]=sin(x+π/6)=1/4
sin^2(π/3-x)=sin^2[π/2-(x+π/6)]=cos^2(x+π/6)=1-sin^2(x+π/6)=1-1/16=15/16
所以sin(5π/6-x)+sin^2(π/3-x)=1/4+15/16=19/16
======以下答案可供参考======
供参考答案1:
sin(5π/6 -x) = sin(x+π/6)= 1/4，两角互补
cos(π/3 -x) = sin(x+π/6)= 1/4，；两角互余
则sin^2 (π/3 -x) = 15/16，则
sin(5π/6 -x)+sin^2 (π/3 -x)= 1/4 +15/16 = 19/16