NIMCET 2016 Question Paper with solutions

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Question : 69 of 120

Marks: +1, -0

If cos θ =

5/{13}

,

{3π}/2

< θ < 2π , then

tan 2θ

is ;

${-120}/{119}$
${-120}/{169}$
${119}/{169}$
${120}/{119}$

Solution:

Concept:

\tan 2 θ=\;{2 \tan θ}/{1-\tan ^{2} θ}

\cos θ=\;{\;\text " base "\;}/{\;\text " hypotenuse "\;}

\tan θ=\;{\;\text " perpendicular "\;}/{\;\text " base "\;}

\;\text " Hypotenuse "\;^{2}=\;\text " Perpendicular "\;^{2}+\;\text " Base "\;^{2}

\cos θ=\;{5}/{13}, \;{3 π}/{2}<θ<2 π

From above

θ

lies in the fourth quadrant so the

\tan θ

will be negative
Hypotenuse

=13

Base

=5

Perpendicular

=√{13^{2}+5^{2}}=± 12

\tan θ=\;{\;\text " perpendicular "\;}/{\;\text " base "\;}

\tan θ=\;{-12}/{5}, \tan θ

is negative in the fourth quadrant

\tan 2 θ=\;{\;{2 ×-12}/{5}}/{1-\;{-12^{2}}/{52}}

\tan 2 θ=\;{120}/{119}

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