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

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

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).

If area of A B C() and angle C are given and if the side c opposite to given angle is minimum, then a=sqrt((2)/(sinC)) (b) b=sqrt((2)/(sinC)) a=sqrt((4)/(sinC)) (d) b=sqrt((4)/(sinC))

In A B C Prove that A B^2+A C^2=2(A O^2+B O^2) , where O is the middle point of B C

Prove that a triangle A B C is equilateral if and only if tanA+tanB+tanC=3sqrt(3)dot

Vertices of a variable acute angled triangle A B C lies on a fixed circle. Also, a ,b ,ca n dA ,B ,C are lengths of sides and angles of triangle A B C , respectively. If x_1, x_2a n dx_3 are distances of orthocenter from A ,Ba n dC , respectively, then the maximum value of ((dx_1)/(d a)+(dx_2)/(d b)+(dx_3)/(d c)) is -sqrt(3) b. -3sqrt(3) c. sqrt(3) d. 3sqrt(3)

If tan^3A+tan^3B+tan^3C=3tanA* tanB*tanC , then prove that triangle ABC is an equilateral triangle.

If C_1: x^2+y^2=(3+2sqrt(2))^2 is a circle and P A and P B are a pair of tangents on C_1, where P is any point on the director circle of C_1, then the radius of the smallest circle which touches c_1 externally and also the two tangents P A and P B is 2sqrt(3)-3 (b) 2sqrt(2)-1 2sqrt(2)-1 (d) 1

If tan A =cot B where A and B are acute angles prove that A+B= 90 ^(@)