Найдите значение выражения:
(sin6°·cos12°·sin24°·cos48°)/(sin138°·sin102°·cos84°·cos66°)
(sin6°·cos12°·sin24°·cos48°)/(sin138°·sin102°·cos84°·cos66°)
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Verified answer
sin138*sin102*cos84cos66=sin(90+48)*sin(90+12)*cos(90-6)*cos(90-24)=0
=cos48*cos12*sin6*sin24
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sin6*sin24*cos12*cos48=1/2*(cos18-cos30+cos36+cos60)/sin6*sin24*cos12*cos48=1/2*(cos18-cos30+cos36+cos60)=1