If in a triangle the bisector of the side c be perpendicular to the side b, prove that: 2.tan(A)+tan(C)=0

Asked by prakharagarwal1405 | 12th Jun, 2014, 08:52: PM

Expert Answer:

D space i s space t h e space m i d p o i n t space o f space A B space a n d space angle A C D equals 90 degree S o space angle B C D space equals space C space minus space 90 degree a n d space angle A D C space equals space 90 degree space minus space A  angle B D C equals space space 90 degree space plus space A  N o w space f r o m space f o r m u l a comma space open parentheses m plus n close parentheses. c o t space theta space equals space m space c o t space alpha space minus space n space c o t space beta w h e r e space m space equals space n space equals space c over 2 comma space theta space equals space 90 degree space plus space A comma space alpha space equals space 90 degree comma space beta space equals space space C space minus space 90 degree  s u b s t i t u t e space t h e space a b o v e space v a l u e s comma space w e space g e t  open parentheses c over 2 plus c over 2 close parentheses c o t space open parentheses 90 degree space plus space A close parentheses equals c over 2 space c o t space 90 degree space minus c over 2 space c o t space C minus 90 degree s i m p l i f i n g space a b o v e space e q u a t i o n space g i v e s  minus c space t an space A equals space 0 space plus space c over 2 space tan space C 2 space tan space A space plus thin space tan space C space equals space 0  H e n c e space P r o v e d

Answered by Dharma Teja | 16th Jun, 2014, 10:22: AM

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