1. If a+b=1,c+d=1 and a-b= $$\frac{d}{c}$$ then the value of $$c^{2}-d^{2}$$ is
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By: anil on 05 May 2019 02.57 pm
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 : => $$(c-d)(c+d) = 1 * frac{b}{a}$$ => $$c^2 - d^2 = frac{b}{a}$$
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