三角函数诱导公式已知sin(x+π/6）=-3/5,sin²（π/3-x)-sin(5π/6-x)的值过程详细点

三角函数诱导公式已知sin(x+π/6）=-3/5,sin²（π/3-x)-sin(5π/6-x)的值过程详细点
三角函数诱导公式
已知sin(x+π/6）=-3/5,sin²（π/3-x)-sin(5π/6-x)的值过程详细点

三角函数诱导公式已知sin(x+π/6）=-3/5,sin²（π/3-x)-sin(5π/6-x)的值过程详细点
∵sin²（π/3-x)-sin(5π/6-x)
=sin²[π/2－（x+π/6）]－sin[π-(x+π/6)]
= cos²（x+π/6）－sin(x+π/6）
∵sin(x+π/6）=-3/5
sin²(x+π/6）＋cos²（x+π/6）=1
∴cos²（x+π/6）=1-（9/25）=16/25
∴sin²（π/3-x)-sin(5π/6-x)
=cos²（x+π/6）－sin(x+π/6）
=16/25+3/5=31/25

sin(x+π/6)=-3/5
∴sin²(π/3-x)-sin(5π/6-x)
=1-cos²(x-π/3)-cos(-π/3+x)
=-cos²(x-π/3)-cos(x-π/3)+1
∵sin(x+π/6)=cos(π/3-x)=cos(x-π/3)=-3/5
∴原式=-(9/25)+3/5+1=31/25
谢谢