Question

If cos (A+B)/cos (A-B) = sin (C+D)/sin (C-D) prove that tanA tanB tan C + tanD=0.

cos(A-B)-cos(A+B)]/[cos(A-B)+cos(A+B)]=[sin(C-D)-sin(C+D)]/[sin(C-D)+sin(C+D)] why this thing happens

Answer 1

Cos (A+B)/ cos(A-B) = sin (C+D)/sin (C-D)

cos( A+B) sin (C-D) = sin (C+D) cos (A-B)

(cos A cos B-sin A sin B)( sin C cos D- cos C sin D) = (sin C cos D+ cos c sin D)(cos A cosB + sin A SinB)

multiply

cos A cos B sin C cos D - cos A cos B cos C sin D - sin A sin B sin C cos D + sin A sin B cos C sin D = sin C cos D cos A cos B + sin C cos D sin A sin B + cos C sin D cos A cos B+ cos C sin D sin A sin B

Rearrange and divide by cos A cos B cos C cos D

you will get

please check the attachment