`C F` is the internal bisector of angle `C` of ` A B C` , then `C F` is equal to (a) `(2a b)/(a+b)cos(C/2)` (b) `(a+b)/(2a b)cosC/2` (c) `( bsinA)/(sin(B+C/2))` (d) none of these

(ii) (b-c) cos( A/2) = a sin ((B-C)/2)

If a,b,c are in H.P , b,c,d are in G.P and c,d,e are in A.P. , then the value of e is (a) (ab^(2))/((2a-b)^(2)) (b) (a^(2)b)/((2a-b)^(2)) (c) (a^(2)b^(2))/((2a-b)^(2)) (d) None of these

In A B C , the median A D divides /_B A C such that /_B A D :/_C A D=2:1 . Then cos(A/3) is equal to (sinB)/(2sinC) (b) (sinC)/(2sinB) (2sinB)/(sinC) (d) none of these

A, B and C are interior angles of a triangle ABC, then sin ((B + C)/(2)) =

With usual notations, in triangle A B C ,acos(B-C)+bcos(C-A)+c"cos"(A-B) is equal to(a) (a b c)/R^2 (b) (a b c)/(4R^2) (c) (4a b c)/(R^2) (d) (a b c)/(2R^2)

If a ,b ,and c are in A.P., then a^3+c^3-8b^3 is equal to (a). 2a b c (b). 6a b c (c). 4a b c (d). none of these

In triangle A B C ,/_A=30^0,H is the orthocenter and D is the midpoint of B C . Segment H D is produced to T such that H D=D T The length A T is equal to (a). 2B C (b). 3B C (c). 4/2B C (d). none of these

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

(ix) (a^(2) sin (B-C))/(sinA) + (b^(2) sin (C-A))/(sin B) + (c^(2) sin (A-B))/(sin C)=0

(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))