Question

if A , B ,C are interioir angles of a triangle,then (1) tan(B+C/2) = cot(A/2) (2)sin(B+C/2) = cos(A/2)

Answer 1

Answer:

A + B + C = 180°

Therefore ,

B + C = 180 - A

(B + C) / 2 = (180 - A ) / 2

(B + C) / 2 = 90 - (A / 2)

Hence R.H.S. :- cos (A / 2) = sin [ 90 - (A / 2) ]

= sin [ (B+C) / 2 ] ----- As 90 - (A / 2) = 2 (B+C) / 2 ]

Therefore ,

cos (A / 2) = sin [ (B+C) / 2 ]

Hence proved.