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If alpha and beta are the roots of the equation t^2 - 2t + 2 =0 And [ (x+ alpha)^n - (x+beta)^n]/ alpha - beta = Sin ntheta/(Sintheta)^n Then prove that x= cot theta - 1

 
If alpha and beta are the roots of the equation
t^2 - 2t + 2 =0    And [ (x+ alpha)^n - (x+beta)^n]/ alpha - beta = Sin ntheta/(Sintheta)^n
Then prove that 
x= cot theta - 1

Grade:11

1 Answers

Mikshala A U
13 Points
5 years ago
We have, alpha+beta=2(1)
 Substituting n=2 in the exp,
(X+alpha)^2-(x+beta)^2/apha-beta=sin 2theta/sin^2theta
x^2+2xalpha+alpha^2-x^2-2xbeta-beta^2/alpha-beta= 2(sintheta)(costheta)/sin^2(theta)
2x+alpha+beta=2cot(theta)
Substituting (1)
x=cot(theta)-1.

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