ABC is a triangle inscribed in a circle centre O Let alpha BAC where 450 lt alpha lt 90 Let beta lt ...........

Mathematics (NDA) Coordinate Geometry

ABC is a triangle inscribed in a circle centre O. Let α = $\angle$ BAC,where 45⁰ < α < 90 . Let β =< BOC.Which one of the following correct?

$cos\beta =\frac{1-tan^{2}\alpha }{1+tan^{2}\alpha}$

$cos\beta =\frac{1+tan^{2}\alpha }{1-tan^{2}\alpha}$

$cos\beta =\frac{2tan\alpha }{1+tan^{2}\alpha}$

$sin\beta =2sin^{2}\alpha$

$\beta =2\alpha\: (by \: circle's\: theorem)$
$cos\beta =cos2\alpha =\frac{1-tan^{2}\alpha }{1+tan^{2}\alpha }$

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