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UPSC NDA I 2016 Mathematics Solved Paper

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For the next two (2, items that follow :

Given that tanα and tanβ are the roots of the equation

x^2+bx+c=0

with

b \neq 0

.

[NDA I 2016]

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Question : 38 of 120

Marks: +1, -0

What is tan (α + β) equal to

$b(c-1)$
$c(b-1)$
$c(b-1)^{-1}$
$b(c-1)^{-1}$

Solution:

x^{2}+bx+c=0

b\neq 0

∵

\tan\alpha

and

\tan\beta

are roots of equation

\because\tan\alpha+\tan\beta=\frac{-b}{1}=-b

, .....(1)

\therefore\tan\alpha\tan\beta=\frac{c}{1}=c

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

=b(c-1)^{-1}

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