If the line `x=y=z` intersect the line `s in Adotx+s in Bdoty+s in Cdotz=2d^2,s in2Adotx+s in2Bdoty+s in2Cdotz=d^2,` then find the value of `sinA/2dotsinB/2dotsinC/2w h e r eA ,B ,C` are the angles of a triangle.

IF in Delta ABC , sin A/2 sin C /2 =sin B/2 and 2s is the perimeter of the triangle then s is

If the line passing through the focus S of the parabola y=a x^2+b x+c meets the parabola at Pa n dQ and if S P=4 and S Q=6 , then find the value of adot

In triangle ABC, prove that the maximum value of tan(A/2)tan(B/2)tan(C/2)i s R/(2s)

If S_k=(1+2+3+...k)/k then find the value of S_1^2+S_2^2+....S_n^2

Area bounded by the curve x y^2=a^2(a-x) and the y-axis is (pia^2)/2s qdotu n i t s (b) pia^2s qdotu n i t s (c) 3pia^2s qdotu n i t s (d) None of these

In a scalene triangle A B C ,D is a point on the side A B such that C D^2=A D D B , sin s in A S in B=sin^2C/2 then prove that CD is internal bisector of /_Cdot

If the extremities of the base of an isosceles triangle are the points (2a ,0) and (0, a), and the equation of one of the side is x=2a , then the area of the triangle is (a) 5a^2s qdotu n i t s (b) (5a^2)/2s qdotu n i t s (c) (25 a^2)/2s qdotu n i t s (d) none of these

Let A B C be a triangle right-angled at Aa n dS be its circumcircle. Let S_1 be the circle touching the lines A B and A C and the circle S internally. Further, let S_2 be the circle touching the lines A B and A C produced and the circle S externally. If r_1 and r_2 are the radii of the circles S_1 and S_2 , respectively, show that r_1r_2=4 area ( A B C)dot

The area bounded by the curves y=x e^x ,y=x e^(-x) and the line x=1 is 2/e s qdotu n i t s (b) 1-2/e s qdotu n i t s 1/e s qdotu n i t s (d) 1-1/e s qdotu n i t s

If the curves x^(2)-y^(2)=4 and xy = sqrt(5) intersect at points A and B, then the possible number of points (s) C on the curve x^(2)-y^(2) =4 such that triangle ABC is equilateral is