If angle C of triangle ABC is `90^0,` then prove that `tanA+tanB=(c^2)/(a b)` (where, `a , b , c ,` are sides opposite to angles `A , B , C ,` respectively).

In right angled triangle ABC, right angled at C, show that tanA+tanB=(c^2)/(ab) .

In a triangle ABC,/_C=(pi)/(2)* If tan ((A)/(2)) and tan((B)/(2)) are the roots of the equation ax^(2)+bx+c=0,(a!=0), then the value of (a+b)/(c) (where a,b,c, are sides of opposite of angles A,B,C, respectively is

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 .

If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression (a)/(c) sin 2C + (c)/(a) sin 2A is

In triangle ABC , if angle C=(pi)/(2) , then prove sin(A-B)=(a^2-b^2)/(a^2+b^2) .

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)

If the angles A,B and C of a triangle ABC are in an A.P with a positive common difference such that the smallest angle is one third of the largest angle, and the sides a, b and c are the sides opposite to the angles A ,B and C such that (a)/(sin A)=(b)/(sin B)=(c)/(sin C) then the ratio of the longest side to that of the shortest side will be