cos6 cos42 cos66 cos78cos6*cos54*cos66=1/4 * cos18why? thanks

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cos6 cos42 cos66 cos78cos6*cos54*cos66=1/4 * cos18why? thanks
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cos6 cos42 cos66 cos78cos6*cos54*cos66=1/4 * cos18why? thanks
cos6 cos42 cos66 cos78
cos6*cos54*cos66=1/4 * cos18
why? thanks

cos6 cos42 cos66 cos78cos6*cos54*cos66=1/4 * cos18why? thanks
解 据已知恒等式:
cosx*cos(60°+x)*cos(60°-x)=cos(3x)/4
cos6°*cos42°*cos66°*cos78°= cos6°*cos66°*[ cos18°*cos42°*cos78°/ cos18°]
= cos6°*cos66°*cos54°/(4 cos18°)
= cos18°/(16 cos18°)=1/16.