The base of a triangle is divided into t...

The base of a triangle is divided into three equal parts. If `t_1, t_2,t_3` are the tangents of the angles subtended by these parts at the opposite vertex, prove that `(1/(t_1)+1/(t_2))(1/(t_2)+1/(t_3))=4(1+1/t_2^2)dot`

Similar Questions

Explore conceptually related problems

if the normal at the point t_(1) on the parabola y^(2) = 4ax meets the parabola again in the point t_(2) then prove that t_(2) = - ( t_(1) + 2/t_(1))

Solve: (4t)/(t^2-25)=1/(5-t)

If t_1a n dt_2 are the ends of a focal chord of the parabola y^2=4a x , then prove that the roots of the equation t_1x^2+a x+t_2=0 are real.

Integrate the functions e^(t)((1)/(t)-(1)/(t^(2)))

Differentiate the following : h(t) = (t - (1)/(t) )^(3//2)

If the normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that t_2 2geq8.

Prove that the point of intersection of the tangents at t_(1) and t_(2) on the parabola y^(2) = 4ax is (at1t2,a(t1+t2))

If the normals at points t_1a n dt_2 meet on the parabola, then t_1t_2=1 (b) t_2=-t_1-2/(t_1) t_1t_2=2 (d) none of these