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

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

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
A
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