If `A` and `C` are two angles such that `A+C=(3pi)/4` then `(1+cotA)(1+cotC)=`

The sides of a triangle are in AP. If the angles A and C are the greatest and smallest angle respectively, then 4 (1- cos A) (1-cos C) is equal to

If A,B and C are the angle of a non-right angled Delta ABC the value of |{:(tanA,1,1),(1,tanB,1),(1,1,tanC):}| is

Prove that tan^(-1) 2 + tan^(-1) 3 = (3pi)/4

In the triangle ABC, lines OA,OB and OC are drawn so that angles OAB, OBC and OCA are each equal to omega , prove that cotomega=cotA+cotB+cotC

vec(a)_|_vec(b) and vec(c),|vec(a)|=2,|vec(b)|=3,|vec( c )|=4 . The angle between vec(b) and vec( c ) is (2pi)/(3) then |[vec(a) vec(b) vec( c )]| = …………

Prove the following identities. where the angles involved are acute angles for which the expressions are defined. ((1+tan^(2)A)/(1+cot^(2)A))=((1-tanA)/(1-cotA))^(2)=tan^(2)A

If the angle between two lines is (pi)/(4) and slope of one of the lines is (1)/(2) , find the slope of the other line.

Prove the following identities. where the angles involved are acute angles for which the expressions are defined. (cosA-sinA+1)/(cosA+sinA-1)=cosecA+cotA , using the identity cosec^(2)A=1+cot^(2)A .

Suppose a, b, c, in R and abc = 1, if A = [[3a, b, c ],[b, 3c, a ],[c, a, 3b]] is such that A ^(T) A = 4 ^(1//3) I and abs(A) gt 0, the value of a^(3) + b^(3) + c^(3) is

Prove that the triangle ABC is equilateral if cotA+cotB+cotC=sqrt3