Using vectro mehod, prove that in a `/_\ABC, a/(sinA),b/(sinB)=c/(sinC)` where a,b,c are the lenths of the sides opposite to the angles A,B and C respectively of `/_\ABC`.

Prove by the method of vectors that in a triangle a/(sin A)=b/(sinB)=c/(sinC) .

In Delta ABC,a,b,c are the opposite sides of the angles A,B and C respectively,then prove (sin B)/(sin(B+C))=(b)/(a)

Delta=|(1,(4sinB)/b,cosA),(2a,8sinA,1),(3a,12sinA,cosB)| is (where a, b, c are the sides opposite to angles A, B, C respectively in a triangle)

In a triangle ABC with fixed base BC, the vertex A moves such that cos B + cos C = 4 sin^(2) A//2 If a, b and c denote the lengths of the sides of the triangle opposite to the angles A,B and C respectively, then

Let (sinA)/(sinB)=(sin(A-C))/(sin(C-B)) , where A , B, C are angles of a triangle ABC. If the lengths of the sides opposite these angles are a,b,c respectively, then

Prove that in ABC,tan A+tan B+tan C>=3sqrt(3) where A,B,C are acute angles.

The largest side of a triangle ABC that can be inscribed in acrcle so that (a^(3)+b^(3)+c^(3))/(sin^(3)A+sin^(3)B+sin^(3)C)=64 is (where a,b,c are lengths of sides opposite to vertices A,B,C of the triangle ABC respectively)

If angle C of triangle ABC is 90^(@) ,then prove that tan A+tan B=(c^(2))/(ab) (where,a,b,c, are sides opposite to angles A,B,C, respectively).

Consider a triangle ABC and let a,b and c denote the lengths of the sides opposite to vertices A,B and C respectively.If a=1,b=3 and C=60^(@), the sin^(2)B is equal to