已知sin(x+π/6)=1/3,求sin(7π/6+x)+cos²(5π/6-x)的值
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已知sin(x+π/6)=1/3,求sin(7π/6+x)+cos²(5π/6-x)的值
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![已知sin(x+π/6)=1/3,求sin(7π/6+x)+cos²(5π/6-x)的值](/uploads/image/z/2179488-48-8.jpg?t=%E5%B7%B2%E7%9F%A5sin%28x%2B%CF%80%2F6%29%3D1%2F3%2C%E6%B1%82sin%287%CF%80%2F6%2Bx%29%2Bcos%26sup2%3B%285%CF%80%2F6-x%29%E7%9A%84%E5%80%BC)
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
=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
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