Prove that |(1,1,1),(bc,ca,ab),(b+c, c+a, a+b)| = (a-b)(b-c)(c-a)
Using the property of determinants prove that {:|( 3a,-a+b,-a+c),( -b+a, 3b,-b+c) ,( -c+a,-c+b,3c) |:} = 3( a+b+c) ( ab+bc+ca)
Prove that {:[(1,ab,a+b),(1,bc,b+c),(1,ca,c+a):}]=(a-b)(b-c)(c-a)
Prove that a^(2)+b^(2)+c^(2)=2(ab cos C +bc cosA +ca cos B)
Prove that |(1,a^2,bc),(a,b^2,ca),(1,c^2,ab)|=(a-b)(b-c)(c-a)
Prove that |(-a^2,ab,ac),(bc,-b^2,bc),(ca,cb,-c^2)|=4a^(2)b^(2) c^(2) .
Prove that A(BC)=(AB)C
In the figure, an isosceles triangle ABC with AB=AC circumscribes a circle. Prove that the point of contact P bisects the base BC.
ABC is a right triangle right angled at C. Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB. Prove that (i) pc = ab (ii) (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2)) .
Prove that abs{:(a^(2) + 1, ab , ac),(ab, b^(2) + 1, bc),(ca, cb, c^(2) +1):}=1 + a^(2) + b^(2) +c^(2)
