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/(t2 2))dot`

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)))

The base of a triangle is divided into three equal parts. If t_(1), t_(2), t_(3) be the tangent sof 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)))

The bae of a triangle is divided into three equal parts. If t_(1), t_(2), t_(3) be the tangent sof the angles subtended by these parts at the opposite vertex, prove that : ((1)/(t_(1))+ (1)/(t_(2)))((1)/(t _(1))+(1)/(t _(3)))=4(1+(1)/(t_(1)^(2)))

The base of a triangle is divided into 3-equal part. If t_(1), t_(2), t_(3) be the tangents of the angles subtended by these parts at opposite vertex then of ((1/t_(1) + 1/t_(2))(1/t_(2) + 1/t_(3)))/((1+1/t_(2)^(2))) =

Find the are of triangle whose vertex are: (at_(1),(a)/(t_(1)))(at_(2),(a)/(t_(2)))(at_(3),(a)/(t_(3)))

If t_n=1/4(n+2)(n+3) for n=1,2,3, , then 1/(t_1)+1/(t_2)+1/(t_3)++1/(t_(2003))=

The normal at a point t_1 on y^2 = 4ax meets the parabola again in the point t_2 . Then prove that t_1 t_2 + t_1^2 + 2=0

If the time taken by a particle moving at constant acceleration to travel equal distances along a straight line are t_(1), t_(2), t_(3) respectively prove that (1)/(t_(1))-(1)/(t_(2))+(1)/(t_(3))=(3)/(t_(1)+t_(2)+t_(3)) .

If the orthocentre of the triangle formed by the points t_1,t_2,t_3 on the parabola y^2=4ax is the focus, the value of |t_1t_2+t_2t_3+t_3t_1| is