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设α为锐角若cos(α+π/3)=1/5则cos(α-π/6)=
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设α为锐角 若cos (α+π/3)=1/5则cos(α-π/6)=
▼优质解答
答案和解析
cos(α-π/6)=cos(α-π/2+π/3)
=cos(-π/2+α+π/3)
=cos[-(π/2-α-π/3)]
=cos(π/2-α-π/3)
=cos[π/2-(α+π/3)]
=sin(α+π/3)
=√[1-cos² (α+π/3)]
=√[1-(1/5)²]
=(2√6)/5
=cos(-π/2+α+π/3)
=cos[-(π/2-α-π/3)]
=cos(π/2-α-π/3)
=cos[π/2-(α+π/3)]
=sin(α+π/3)
=√[1-cos² (α+π/3)]
=√[1-(1/5)²]
=(2√6)/5
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