Prove that in case of expansion of solid `beta = 2alpha`.

What are the co-efficient of expansion of solid? How are they related?

Prove that the locus of the points of intersection of the lines x cos alpha + y sin alpha = a and x sin alpha - y cos albha = b is a cicle, whatever may be alpha

Prove that (cos alpha-cos beta)^2+(sin alpha-sin beta)^2=4sin^2((alpha-beta)/2)

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)

What is the transition temperature of conver-sion of Alpha - sulpher into beta sulpher and vice versa? Write the common formula of these forms?

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)

What is the relation between alpha and beta ?

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 .