If a, B AND C ARE THE INTERIOR ANGLES OF A TRIANGLE ABC THEN PRO THAT 
Tan(B+C/2)=cot (a/2)

Asked by Sanmit Ratnaparkhi | 12th Aug, 2014, 07:23: PM

Expert Answer:

I f space A comma space B space a n d space C space a r e space i n t e r i o r space a n g l e s space o f space a space t r i a n g l e space t h e n space s u m space o f space a n g l e s space i s space 180 to the power of o A plus B plus C equals straight pi rightwards double arrow straight B plus straight C equals straight pi minus straight A  Tan space open parentheses fraction numerator straight B plus straight C over denominator 2 end fraction close parentheses equals Tan space open parentheses fraction numerator straight pi minus straight A over denominator 2 end fraction close parentheses equals Tan space open parentheses straight pi over 2 minus straight A over 2 close parentheses  We space know space that space Tan space open parentheses 90 space minus straight theta close parentheses equals Cot space straight theta  therefore Tan space open parentheses straight pi over 2 minus straight A over 2 close parentheses equals Cot space open parentheses straight A over 2 close parentheses

Answered by Dharma Teja | 13th Aug, 2014, 07:34: AM