SSC CHSL 10 Jan 2017 Shift 1 Paper

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Question : 58 of 100

Marks: +1, -0

If

cosec^4A-cosec^2A=x

, then value of x is?

$tan^4A + tan^2A$
cot^4A + cot^2A
cot^4A − cot^2A
tan^4A − tan^2A

Solution:

Expression :

cosec^4A-cosec^2A=x

=

cosec^2A(cosec^2A − 1)

=

cosec^2A(1/{sin^2A} − 1)

=

cosec^2A({1-sin^2A}/{sin^2A})

=

cosec^2A({cos^2A}/{sin^2A}

=

cosec^2A ({cot^2A})

∵

cosec ^2A − cot ^2A = 1

=

(cot^2A + 1)cot A

=

cot^4A + cot^2 A

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