Trigonometry Problem

[Nupur]

Hi,

i hav a problem which i am unable to solve. it is from the chapter on trigonometry

 

here goes:

 

A vertical rod is fixed in a horizontal rectangular field ABCD. The angular elevations of its top from A, B, C and D are alpha, beta, gamma and delta respectively. Show that:

cot^2 alpha - cot^2 beta=cot^2 delta - cot^2 gamma

 

plzz help me with this and post the solution as soon as possible

[grayfalcon89]

I'm guessing since angle AB are supplementary and you have cos x = - cos (180-x), you can probably brute force to get the desired expression.

 

Not sure about it though. Haven't worked the whole problem out.

[EvoN1020v]

I don't know if this will help: [math]cot^{2}x = \frac{cos^{2}x}{sin^{2}x}[/math] or [math]\frac{csc^{2}x}{sec^{2}x}[/math] or [math]cot^{2}x = 1 + tan^{2}x[/math].

[s pepperchin]

Are you saying that the field is in the X-Y direction and the pole sticks up in the Z direction with the angles being from the corners of the rectangle to the top of the pole?