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Let alpha and beta be the roots of the ...

Let `alpha` and `beta` be the roots of the quadratic equation `x sin^(2) theta -x (sin theta cos theta + 1) + cos theta =0 (0le thetale 45^(@)) and alpha le beta` . Then`underset(n =0)overset(oo)sum(alpha^(n)+((-1)^(n))/(beta^(n)))` is to equal to

A

`(1)/(1 + cos theta) +(1)/(1- sin theta)`

B

`(1)/( 1+ cos theta ) - (1)/(1- sin theta)`

C

`(1)/( 1- cos theta)+(1)/(1 + sin theta)`

D

`(1)/(1- cos theta)- (1)/(1+ sin theta)`

Text Solution

Verified by Experts

The correct Answer is:
C
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