NIMCET 2018 Question Paper with solutions

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Question : 31 of 120

Marks: +1, -0

The value of cot

(cosec^{-1}5/3 + tan^{-1} 2/3)

is

6/17
3/17
4/17
5/17

Solution:

We have,
cot

(cosec^{-1}5/3 + tan^{-1} 2/3)

= cot

[tan^{-1} 1/√{(5/3)^2-1} + tan^{-1}2/3]

[\Since \cosec^{-1}x = tan^{-1}1/√{x^2-1}]

= cot

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

= cot

(tan^{-1}({3/4+2/3}/{1-3/4×2/3}))

= cot

(tan^{-1}{17}/6)

cot

(cot^{-1}6/{17})

=

6/{17}

[\Since \tan^{-1}x=cot^{-1}1/x]

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