已知5sina=7sin(a-2b) 求证6tanb-tan(a-b)=0

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已知5sina=7sin(a-2b) 求证6tanb-tan(a-b)=0
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已知5sina=7sin(a-2b) 求证6tanb-tan(a-b)=0
已知5sina=7sin(a-2b) 求证6tanb-tan(a-b)=0

已知5sina=7sin(a-2b) 求证6tanb-tan(a-b)=0
5sina
=5sin[(a-b)+b]
=5sin(a-b)cosb+5cos(a-b)sinb
=7sin(a-2b)
=7sin[(a-b)-b]
=7sin(a-b)cosb-7cos(a-b)sinb
∴12cos(a-b)sinb-2sin(a-b)cosb=0
两边同除以2cos(a-b)cosb得到:
6tanb-tan(a-b)=0