`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)

If a ,b ,c denote the lengths of the sides of a triangle opposite to angles A ,B ,C respectively of a A B C , then the correct relation among a ,b , cA ,Ba n dC is given by (b+c)sin((B+C)/2)=acos b. (b-c)cos(A/2)=asin((B-C)/2) c. (b-c)cos(A/2)=2asin((B-C)/2) d. (b-c)sin((B-C)/2)="a c o s"A/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))

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

In any Delta ABC, prove the following: (a+b+c)(cos A+cos B+cos C)=2((a cos^(2))(1)/(2)(A+b cos^(2))(1)/(2)(B+cos^(2))(1)/(2)C)

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))

If : A+B+C= pi "then" : 1 - sin^(2)""(A)/(2) - sin^(2)""(B)/(2)+ sin^(2)""(C)/(2)= A) 2cos""(A)/(2) * cos sin ^(2)""(B)/(2) + sin^(2)""(C)/(2) B) 2 cos ""(B)/(2)* cos ""(B)/(2) * sin""(C)/(2) C) 2 cos ""(C)/(2)* cos ""(A)/(2) * sin""(B)/(2) D) 2 cos ""(A)/(2)* cos ""(B)/(2) * sin""(C)/(2)

(1+cos A*cos(B-C))/(1+cos C*cos(A-B))=(b^(2)+c^(2))/(a^(2)+b^(2))