If $\sec \,\,\alpha $ and ${\rm{cosec}}\;\,\,\alpha $ are the roots of the equation ${x^2} - ax + b = 0$, then

JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

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\sec \,\,\alpha

and

\mathrm{cosec}\;\,\,\alpha

are the roots of the equation

{x^2} - ax + b = 0

, then

View answer and explanation

Correct option: B

{a^2} = b\left( {b + 2} \right)

Option B (

{a^2} = b(b + 2)

) is correct because by using Vieta's formulas to find the sum and product of the roots and then applying the trigonometric identity

{\sin^2 \alpha + \cos^2 \alpha = 1}

, we can derive the given relation.