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UPSC NDA Math Model Paper 2

Comprehension:(Que No. 102 - 103)

Direction: For the next two (2) items that follow:

Given that tan α and tan β are the roots of the equation

x^2 + bx + c = 0

with b ≠ 0

Question : 102 of 120

Marks: +1, -0

What is tan (α + β) equal to?

Solution:

Given:

\tan \alpha \text{ and } \tan \beta

are the roots of the equation

x^2 + bx + c = 0

Sum of roots = tan α + tan β = -b

Product of roots = tan α × tan β = c

\tan (\alpha+\beta)=\frac{\tan \alpha+\tan \beta}{1-(\tan \alpha \times \tan \beta)}

=\frac{-b}{1-c}=\frac{b}{c-1}

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