If Cos(A+B)/cos(A-B) =sin(C+D)/sin(C-D). Prove that tanA tanB tanC + t

1.	If Cos(A+B)/cos(A-B) =sin(C+D)/sin(C-D). Prove that tanA tanB tanC + tanD=0
Answer» cos(a+b) sin(c-d) = cos(a-b) sin(c+d)( cosAcosB - sinAsinB) (sincCosD- cosC sinD) = ( cosAcosB + sinAsinB) (sincCosD+ cosC sinD)- cosA cosBcosCsinD - sinA sinB sinC cosD = cosA cosB cosC sinD + sinA sinB sinC cosD2 cosA cosBcosCsinD + 2sinA sinB sinC cosD=0sinA sinB sinC cosD = - cosA cosBcosCsinDtanA tanB tanC = - tanDtannA tanB tanC + tanD =0

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