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tan alfa,tan bita ,tan gama are the roots of x^3-px^2-r=0 then find 1+tan^2alfa)(1+tan^2bita)(1+tan^2gama) =

tan alfa,tan bita ,tan gama are the roots of x^3-px^2-r=0 then find 1+tan^2alfa)(1+tan^2bita)(1+tan^2gama)=
 

Grade:11

1 Answers

Lab Bhattacharjee
121 Points
8 years ago
Let \text{Let }x^2+1=y \\ x^3-px^2-r=0\implies x^2(x-p)=r\iff(y-1)(x-p)=r \\ \iff x=p+\dfrac r{y-1}=\dfrac{py+r-p}{y-1} \\ \text{Set the value of } x \text{ in the given equation} \\ \text{Now, we need the product of the roots of the new cubic equation in } y

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