Find a quadratic equation whose sum and product of the roots are the values of the expressions cosec 10 -3sec - Maths - Complex Numbers and Quadratic Equations

Question

Find a quadratic equation whose sum and product of the roots are
the values of the expressions cosec   10 ° - 3 sec  
10 ° and (0 5 cosec 10° – 2 sin 70°) respectively
Also express the roots of this quadratic in terms of tangent of an
angle lying in (0, π/2)

Ankita Agarwal · Accepted Answer

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Find a quadratic equation whose sum and product of the roots are the values of the expressions cosec 10 ° - 3 sec 10 ° and (0.5 cosec 10° – 2 sin 70°) respectively. Also express the roots of this quadratic in terms of tangent of an angle lying in (0, π/2).

Find a quadratic equation whose sum and product of the roots are the values of the expressions $(cosec 10 ° - \sqrt{3} \sec 10 °)$ and (0.5 cosec 10° – 2 sin 70°) respectively. Also express the roots of this quadratic in terms of tangent of an angle lying in (0, π/2).