Number of triangles `A B C` if `tanA=x ,tanB=x+1,a n dtanC=1-x` is ________

Column I Column II In A B C , if cos24+cos2B+cos2C=-1 then we can conclude that triangle is p. Equilateral triangle In A B C if tanA >0,tanB >0a n dtanAtanB 0,cotB >0a n dcotAcotB<1, then triangle is s. Obtuse angled triangle

The number of triangles that the four lines y = x + 3, y = 2x + 3, y = 3x + 2, and y + x = 3 form is (a) 4 (b) 2 (c) 3 (d) 1

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

Prove that there exist exactly two non-similar isosceles triangles A B C such that tanA+tanB+tanC=100.

If in a Delta ABC ,tanA+tanB+tanC=6, then cotA cotB cotC=

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

If A+B=45^o ,then tanA+tanB+tanAtanB is:

Let A B C be a triangle such that /_A C B=pi/6 and let a , ba n dc denote the lengths of the side opposite to A , B ,a n dC respectively. The value(s) of x for which a=x^2+x+1,b=x^2-1,a n dc=2x+1 is(are) -(2+sqrt(3)) (b) 1+sqrt(3) 2+sqrt(3) (d) 4sqrt(3)

If A,B,C are the angles of a non right angled triangle ABC. Then find the value of: |[tanA,1,1],[1,tanB,1],[1,1,tanC]|

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