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

If in a triangle A B C ,/_C=60^0, then prove that 1/(a+c)+1/(b+c)=3/(a+b+c) .

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

Let ABC is be a fixed triangle and P be veriable point in the plane of triangle ABC. Suppose a,b,c are lengths of sides BC,CA,AB opposite to angles A,B,C, respectively. If a(PA)^(2) +b(PB)^(2)+c(PC)^(2) is minimum, then point P with respect to DeltaABC is

If an a triangle A B C , b=3ca n d C-B=90^0, then find the value of tanB

The area of a triangle A B C is equal to (a^2+b^2-c^2) , where a, b and c are the sides of the triangle. The value of tan C equals

Prove that in A B C ,tanA+tanB+tanCgeq3sqrt(3,) where A , B , C are acute angles.

In any triangle ABC, prove that a cos A+b cos B +c cos C =(8 triangle^(2))/(abc) .

In a triangle A B C prove that a//(a+c)+b//(c+a)+c//(a+b)<2

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.