A jet plane is at a vertical height of h. The angles of depression of two tanks on the ground in the same line with the plane are `alpha and beta (alpha gt beta)`. Prove that the distance between the tanks is `( h (tan alpha - tan beta))/(tan alpha tan beta)`

A bridge across a valley is h metres long. There is a temple in the valley directly below the bridge. The angles of depression of the top of the temple from the two ends of the bridge are alpha and beta . Prove that the height of the bridge above the top of the temple is (h (tan alpha tan beta))/(tan alpha + tan beta) metres.

A building stands on a horizontal plane and is surmounted by a vertical flag-stagg of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are alpha and beta respectively. Prove that the height of the building is (h tan alpha)/(tan beta-tan alpha)

Find the sum to n terms, whose nth term is tan[alpha+(n-1)beta]tan (alpha+nbeta) .

A window of a house is h metres above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite sides of the lane are found to be alpha and beta respectively. Prove that the height of the other house is h(1 + tan alpha cot beta) metres.

Find distance PQ between the points P ( a cos alpha, a sin alpha) and Q ( a cos beta, a sin beta) .

If 3 sin alpha=5 sin beta , then (tan((alpha+beta)/2))/(tan ((alpha-beta)/2))=

A particle thrown over a triangle from one end of a horizontal base falls on the other end of the base after grazing the vertex. If alpha and beta are the base angles of triangle and angle of projection is theta , then prove that ( tan theta = tan alpha + tan beta)

If costheta=(cosalphacosbeta)/(1-sinalphasinbeta) then prove that tan((theta)/(2))=(tan((alpha)/(2))-tan((beta)/(2)))/(1-tan((alpha)/(2))tan((beta)/(2)))

The point of intersection of lines is (alpha, beta) , then the equation whose roots are alpha, beta , is

If the angle of elevation of a cloud from a point h metres above the surface of a lake is alpha and the angle of depression of its reflexion in the lake is beta , prove that the height of the cloud is (h (tan beta + tan alpha))/(tan beta - tan alpha) metres.