To manipulate someone (figuratively); to make someone act according to one's will.
政治家は世論を踊らせるために巧妙な発言をした。
The politician made a clever remark to manipulate public opinion.
彼は取引先をうまく踊らせて有利な条件を引き出した。
He skillfully manipulated the client to extract favorable terms.
広告は消費者の感情を踊らせるように作られていることが多い。
Advertisements are often designed to influence consumers' emotions.
To make someone dance (literally); to cause or allow someone to dance.
先生は子供たちを並べて簡単な振り付けで踊らせた。
The teacher lined up the children and had them dance a simple choreography.
祭りの夜、踊り手を舞台に上げて踊らせた。
On the festival night, they brought the dancers on stage and made them perform.
彼はギターの調子に合わせて犬を踊らせる芸を見せた。
He performed a trick where he made the dog dance to the guitar tune.