請問一下,
(sin(A+B)) / (sin(A-B)) = - ( ( cotA+cotB) / ( cotA-cotB) )
這個應該怎樣prove?
是用交叉相乘嗎?
謝謝!
trigo proving
2009-12-06 6:30 am
回答 (1)
2009-12-06 6:34 am
✔ 最佳答案
Prove sin(A+B) / sin(A-B) = - (cotA+cotB) / (cotA-cotB)
LHS = (sinAcosB + sinBcosA) / (sinAcosB - sinBcosA)
= (sinAcosB/sinAsinB + sinBcosA/sinAsinB) / (sinAcosB/sinAsinB - sinBcosA/sinAsinB)
= (cosB/sinB + cosA/sinA) / (cosB/sinB - cosA/sinA)
= (cotB + cotA) / (cotB - cotA)
= -(cotA + cotB) / (cotA - cotB)
= RHS
收錄日期: 2021-04-23 23:23:39
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