f.4 math X2

if A,B,C are the angles of a triangle, proved that

a) tanA = -tan(B+C)

b)cosA/2 = sin(B+C)/2
SOLUTION
For a triangle A+B+C=180.
B+C=180-A
(a)
RHS
-tan(B+C)
=-tan(180-A)
=tanA (because tan(180-x)=-tanx)
(b)
RHS
=sin(B+C)/2
=sin[(180-A)/2]
=sin[90-(A/2)]
=cos A/2 (because sin(90-x)=cosx)