NIFT UG 2013 Question Paper with solutions

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Question : 46 of 150

Marks: +1, -0

The value of

\tan[\cos^{-1}4/5+\tan^{-1}2/3]

is

$6/17$
$7/16$
$17/6$
None of these

Solution:

\tan[\cos^{-1}4/5+\tan^{-1}2/3]

Let

\cos^{-1}(4/5)=x

\cos(x)=4/5

,

\tanx=\;\;{√{1-\cos^{2}x}}/{\cos(x)}=\;\;{3}/{4}

again,let

\tan^{-1}(2/3)=y

\tan(y)=2/3

we know that

\tan(x+y)={\tanx+\tany}/{1-\tanx⋅\tany

=\;\;{\;\;{3}/{4}+\;\;{2}/{3}}/{1-\;\;{3}/{4}⋅\;\;{2}/{3}}=\;\;{17}/{6}

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