# If #theta# is eliminated from the equation #x=acos(theta-alpha)# and #y=bcos(theta-beta)# then prove that #(x/a)^2+(y/b)^2-(2xy)/(ab)cos(alpha-beta)=sin^2(alpha-beta#)?

##### 2 Answers

Given

then

Inserting in LHS we get

I add here what I see in this family of ellipses given by the .second degree equation

#### Explanation:

I add here what I see in this 4-parameter family of ellipses.

The elimination of

interested readers to know more about these equations.

The second degree equation equation

represents a family of ellipses, bracing the rectangle

The Choice

If

equation

becomes

Degenerate cases:

It represents the diagonals of the enveloping rectangle, with ends

as vertices of the rectangle.a straight line

for

Another form of the equation, without