`cos^2((B-C)/2)/((b+c)^2)+sin^2((B-C)/2)/((b-c)^2)=1/(a^2)`

If a,b,c are sides opposte to the angles A,B , C then which of the following is correct (1)(b+c)cos((A)/(2))=a sin((B+C)/(2))(2)(b+c)cos((B+C)/(2))=a sin((A)/(2))(3)(b-c)cos((B-C)/(2))=a(cos A)/(2)(4)(b-c)cos((A)/(2))=a sin((B-C)/(2))

In triangle ABC,a,b,c are the lengths of its sides and A,B,C are the angles of triangle ABC .The correct relation is given by (a) (b-c)sin((B-C)/(2))=a(cos A)/(2) (b) (b-c)cos((A)/(2))=as in(B-C)/(2)(c)(b+c)sin((B+C)/(2))=a(cos A)/(2)(d)(b-c)cos((A)/(2))=2a(sin(B+C))/(2)

For DeltaABC prove that, (a-b)^(2)cos^(2)""(C)/(2)+(a+b)^(2)sin^(2)""(C)/(2)=c^(2)

Show that (a sin (B-C))/( b^(2) - c^(2)) - ( b sin (C-A))/( c^(2) - a^(2)) - ( c sin ( A- B))/( a^(2) -b^(2))

Prove that (a sin(B-C))/(b^(2)-c^(2))=(b sin(C-A))/(c^(2)-a^(2))=(c sin(A-B))/(a^(2)-b^(2))

(x) (a sin(B-C))/(b^(2)-c^(2)) = (b sin (C-A))/(c^(2)-a^(2)) = (c sin(A-B))/(a^(2)-b^(2))

If A+B+ C =pi , then prove that cos ^(2) (A/2)+ cos ^(2) (B/2) +cos ^(2) (C/2)=2(1+sin . (A)/(2) sin. (B)/(2) sin. (C)/(2))

If A+B+C=180^(@), then prove that cos^(2)(A)/(2)+cos^(2)(B)/(2)+cos^(2)(C)/(2)=2(1+sin(A)/(2)sin(B)/(2)sin(C)/(2))