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cos^(2)theta - sintheta = 1/4 (0^(@) lt ...

`cos^(2)theta - sintheta = 1/4 (0^(@) lt theta lt 360^(@))`

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`30^(@), 150^(@)`
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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