Prove that `a^(2)+ b^(2) +c^(2) +2abclt2,` where a,b,c are the sides of triangle ABC such that `a+b+c=2.`

If tan A and tan B are the roots of abx^2- c^2x + ab= 0 , where a, b, c are the sides of the tnangle ABC, then the value of sin^2 A + sin^2 B + sin^2 C is :

An equilateral triangle PQR is circumscribed about a given DeltaABC. Prove that the maximum area of Delta PQR is 2 Delta + (a^(2) +b^(2)+c^(2))/(2sqrt3)). Where a,b,c are the sides of Delta ABC an Delta is its area.

If tan^(-1) . b/(c+a) + tan^(-1) . (c)/(a + b) = pi/4 where a, b, c , are the sides of Delta ABC",then" Delta ABC is

If A, B, C are interior angles of triangle ABC, prove that :- cos((B+C)/2)=sin(A/2) .

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 ABC, 2ca sin frac(A-B+C)(2) =

Prove that, in any triangle ABC, cos B=(c^2+a^2-b^2)/(2ca) .

In Delta ABC , the ratio a/sin A=b/sinB=c/sinC is not always equal to (All symbols used have usual meaning in a triangle.) a. 2R, where R is the circumradius b. (abc)/(2Delta), where Delta is the area of the triangle c. 2/3 (a^(2)+ b^(2) +c^(2)) ^(1/2) d. ((abc)^(2/3))/((h_(1)h_(2) h_(3))^(1/3)

If Delta = a^(2)-(b-c)^(2), Delta is the area of the Delta ABC then tan A = ?

If A, B, C are interior angles of triangle ABC, prove that :- tan((A+B)/2)=cot "C/2 .