證1-cosAsinBcscC=sinAcosBcscC

2013-12-18 4:37 am
在△ABC中,證1-cosAsinBcscC=sinAcosBcscC

回答 (1)

2013-12-18 5:36 am
✔ 最佳答案
Notice that sin C csc C = 1
LHS = 1 - cosA sinB cscC = sinCcscC - cosAsinBcscC
= cscC (sinC - cosAsinB)
= cscC { sin[180 - (A + B)] - cosAsinB}
= cscC [sin(A + B) - cosAsinB]
=cscC (sinAcosB + cosAsinB - cosAsinB)
=cscCsinAcosB = RHS


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https://hk.answers.yahoo.com/question/index?qid=20131217000051KK00127

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