搜狗做题网求值：以2为底,cos 圆周率/9的对数+以2为底,cos 2圆周率/9的对数+以2为底,cos 4圆周率/9的对数
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求值：以2为底,cos 圆周率/9的对数+以2为底,cos 2圆周率/9的对数+以2为底,cos 4圆周率/9的对数
数学函数题,圆周率约等于3.14
数学函数题,圆周率约等于3.14
原式=log2[cosπ/9*cos2π/9*cos4π/9]
cosπ/9*cos2π/9*cos4π/9
=8sinπ/9*cosπ/9*cos2π/9*cos4π/9/8sinπ/9
=4sin2π/9*cos2π/9*cos4π/9/8sinπ/9
=2sin4π/9*cos4π/9/8sinπ/9
=sin8π/9/8sinπ/9
=sinπ/9/8sinπ/9
=1/8
=2^(-3)
所以原式=-3
cosπ/9*cos2π/9*cos4π/9
=8sinπ/9*cosπ/9*cos2π/9*cos4π/9/8sinπ/9
=4sin2π/9*cos2π/9*cos4π/9/8sinπ/9
=2sin4π/9*cos4π/9/8sinπ/9
=sin8π/9/8sinπ/9
=sinπ/9/8sinπ/9
=1/8
=2^(-3)
所以原式=-3
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