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If sec $α$ and cosec $α$ are the roots of the equation $x^{2} - a x + b = 0,$ then

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a

a2=b(b−2)

b

a2=b(b+2)

c

a2+b2=2b

d

none of these

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detailed solution

Correct option is B

It is given that sec αand cosecα are the roots of the equation x2−ax+b=0∴ sec⁡α+cosec⁡α=a and sec⁡αcosec⁡α=b ⇒ sin⁡α+cos⁡α=asin⁡αcos⁡α and sin⁡αcos⁡α=1b ⇒ sin⁡α+cos⁡α=ab and sin⁡αcos⁡α=1b (sin⁡α+cos⁡α)2=1+2sin⁡αcos⁡α ⇒ a2b2=1+23⇒a2=b(b+2)

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