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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
`sum_(n=0)^(oo)(alpha^(n)+((-1)^(n))/(beta^(n)))` is 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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