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求值:㏒2∧cos20°+㏒2∧cos40°+㏒2∧cos80°
题目详情
求值:㏒2∧cos20°+㏒2∧cos40°+㏒2∧cos80°
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答案和解析
log2(cos20°)+log2(cos40°+log2(cos80°)
=log2(cos20°*cos40°*cos80°)
=log2(sin20cos20cos40cos80/sin20)
=log2(1/2*sin40cos40cos80/sin20)
=log2(1/4*sin80cos80/sin20)
=log2(1/8*sin160/sin20)
=log2(1/8)
=-3
=log2(cos20°*cos40°*cos80°)
=log2(sin20cos20cos40cos80/sin20)
=log2(1/2*sin40cos40cos80/sin20)
=log2(1/4*sin80cos80/sin20)
=log2(1/8*sin160/sin20)
=log2(1/8)
=-3
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