If a+b=1,c+d=1 and a-b= $$\frac{d}{c}$$ then the value of $$c^{2}-d^{2}$$ is

We know that $$a - b = \frac{d}{c}$$ and $$a + b = 1$$

Dividing eqn (1) by (2), we get :

=> $$\frac{a-b}{a+b} = \frac{d}{c}$$

Using componendo and dividendo rule :

=> $$\frac{a-b + a+b}{a+b -(a-b)} = \frac{d+c}{c-d}$$

=> $$\frac{a}{b} = \frac{1}{c-d}$$

=> $$c-d = \frac{b}{a}$$ and it is given that $$c+d = 1$$

=> Multiplying the two equations, we get :

=> $$(c-d)(c+d) = 1 * \frac{b}{a}$$

=> $$c^2 - d^2 = \frac{b}{a}$$