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

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

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

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 hat a , hat b ,a n d hat c are three unit vectors, such that hat a+ hat b+ hat c is also a unit vector and theta_1,theta_2a n dtheta_3 are angles between the vectors hat a , hat b ; hat b , hat ca n d hat c , hat a respectively, then among theta_1,theta_2,a n dtheta_3dot a. all are acute angles b. all are right angles c. at least one is obtuse angle d. none of these

In triangle A B C ,tanA+tanB+tanC=6a n dtanAtanB=2, then the values of tanA ,tanB ,tanC are, respectively (a) 1,2,3 (b) 3,2//3,7//3 (c) 4,1//2 ,3//2 (d) none of these

In a A B C , if tanA:tanB :tanC=3:4:5, then the value of sinA sinB sinC is equal to (a) 2/(sqrt(5)) (b) (2sqrt(5))/7 (2sqrt(5))/9 (d) 2/(3sqrt(5))

Let A,B,C, be three angles such that A=pi/4 and tanB tanC=pdot Find all possible values of p such that A , B ,C are the angles of a triangle.