With usual notion, if in triangle `A B C ,` `(b+c)/(11)=(c+a)/(12)=(a+b)/(13),t h e np rov et h a t` `(cosA)/7=(cosB)/(19)=(cosC)/(25)`

Prove that (b+c)cosA+(c+a)cosB+(a+b)cosC=2sdot

If f(x+2a)=f(x-2a),t h e np rov et h a tf(x)i sp e r iod i cdot

Iff(x)=int_1^x(logt)/(1+t+t^2)dxAAxlt=1,t h e np rov et h a tf(x)f(1/x)dot

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)

Given (b+c)/(11)=(c+a)/(12)=(a+b)/(13) for a DeltaABC with usual notation. If (cos A)/(alpha)=(cos B)/(beta)=(cos C)/(gamma) then the ordered traiad, (alpha,beta,gamma) has a vlaue

With usual notations, in any triangle ABC, prove the following by vector method . (i) a^(2)=b^(2)+c^(2)-2bc cos A (ii) b^(2)=c^(2)+a^(2)-2bc cosB (iii) c^(2)=a^(2)+b^(2)-2bc cosC

In A B C , prove that cosA+cosB+cosClt=3/2dot

If in a triangle A B C , (2cosA)/a+(cos B)/b+(2cosC)/c=a/(b c)+b/(c a) , then prove that the triangle is right angled.

In triangle A B C , if cosA+cosB+cosC=7/4, t h e n R/r is equal to 3/4 (b) 4/3 (c) 2/3 (d) 3/2

Given I_m=int_1^e(logx)^mdx ,t h e np rov et h a t(I_m)/(1-m)+m I_(m-2)=e