Let the plane `(x)/(a)+(y)/(b)+(z)/(c)=1` cut the axes at A, B, C respectively .Prove that the area of the triangle ABC is given by `(1)/(2)sqrt(b^(2)c^(2)+c^(2)a^(2)+a^(2)b^(2))`.

In any triangle ABC, prove that, (b^(2)-c^(2))cot A + (c^(2)-a^(2)) cot B + (a^(2)-b^(2)) cot C=0

If the area of the triangle ABC be triangle , show that, b^(2)sin 2C + c^(2) sin 2B= 4triangle .

a variable plane which is at a constant distance 3p from the origin O cuts the axes at A,B,C. Show that the locus of the centroid of the triangle ABC is x^(-2)+y^(-2)+z^(-2)=p^(-2) .

In triangle ABC prove that tan((A+B)/2)=cot. C/2

Find the value of tan A, if area of Delta ABC is a^(2) -(b-c)^(2).

Prove that for a triangle ABC, (a^2-b^2-c^2) tan A+(a^2-b^2+c^2)tan B=0

Given b=2,c= sqrt3 and A= 30^@, then in-radius of triangle ABC is

In Delta ABC, a, b and A are given and c_(1), c_(2) are two values of the third side c. Prove that the sum of the area of two triangles with sides a, b, c_(1) and a, b c_(2) " is " (1)/(2) b^(2) sin 2A

In any triangle ABC, prove that, c sin((A-B)/2)= (a-b) cos( C/2)

In triangle A B C ,2a csin(1/2(A-B+C)) is equal to