CMAT 2018 Solved Question Paper

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Question : 24 of 100

Marks: +1, -0

If tan A + cot A =

√5

, what is the value of

tan ^3 A + cot^3 A

?

3
$2/√5$
$√5$
2 $√5$

Solution:

tan A +

1/{\tan \A}

=

√5

⇒

tan^3A + cot^3A

can be written as

tan ^3 A + 1/{tan^3 A}

⇒

tan ^3 A + 1/{tan^3 A}

=

({\tan A + 1/{\tan \A})}^3

- 3

( tan A + 1/{\tan \A})

( tan A × 1/{\tan \A})

=

(√5)^3 - 3√5

=

5√5 - 3√5

∴

tan ^3 A + 1/{tan^3 A}

=

2√5

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