Chapter 33, Problem 65E

(a)

To determine

The equations obtained by subtracting those equations that are obtained by multiplication of equation (1) by $\sin \beta$ and equation (2) by $\sin \alpha$.

(b)

To determine

The equation obtained by subtracting those equations that are obtained by multiplication of equation (1) by $\cos \beta$ and equation (2) by $\cos \alpha$.

(c)

To determine

The equation obtained by squaring and adding those equations obtained in part (a) and part (b).

(d)

To determine

To derive: The equation $x^2+y^2-2xy\cos \delta =a^2{\sin }^2\delta$ where $\delta =\alpha -\beta$.

(e)

To determine

To justify: The figure given in the question using the derived equation obtained in part (d)