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

The angle of elevation of the top of a tower as observed from a point on the ground is alpha and on moving 'a' metres towards the tower the angle of elevation is beta .Prove that the height of the tower is (atanalphatanbeta) / (tanbeta-tanalpha)

From a window h m high above the ground in a street, the angles of elevation and depression of the top and foot of the other house on the opposite side of the street as alpha and beta respectively show that height of the opposite house is h(1+tan alpha cos beta)m .

The angles of depression of two consecutive kilometer posts on a straight road as seen from an aeroplane above it are alpha and beta(alpha>beta) .Find the height of the aeroplane above the road.

If 2 tan beta + cot beta = tan alpha , prove that 2 tan (alpha-beta) = cot beta

If alpha and beta are the solution of the equation a tan theta +b sec theta=c ,then show that tan(alpha+beta)=2ac/(a^2-c^2)

If tan^2alpha = 1 + tan^2beta ,then prove that cos^2 beta = cot^2alpha

If cos^2alpha-sin^2alpha=tan^2beta ,show that cos^2beta-sin^2beta=tan^2alpha

If alpha and beta be two acute angles and cos2alpha=(3cos2beta-1)/(3-cos2beta) ,show that tan alpha=sqrt2tanbeta

If tanbeta=(nsinalphacosalpha)/(1-nsin^2alpha) ,show that tan(alpha-beta)=(1-n)tanalpha

An aeroplane flying horizontally at a height of 1.5 km above the ground is observed at a certain point on the earth to subtend an angle 60°. After 15 second its angle of elevation is observed to be 30°. Calculate the speed of aeroplane in Km/h.