SSC CGL 26 Oct 2014 Shift 2 Paper

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Question : 129 of 200

Marks: +1, -0

If tan θ =

1/√{11}

and 0 < θ <

π/2

, then the value of

{cosec^2 θ - sec^2 θ}/{cosec^2 θ + sec^2 θ}

is

$3/4$
$4/6$
$5/6$
$6/7$

Solution:

tan θ =

1/*√{11}

; cot θ =

√{11}

∴

{cosec^2 θ - sec^2 θ}/{cosec^2 θ + sec^2 θ}

=

{1+cot^2θ-(1+tan^2 θ)}/{1+cot^2 θ + 1 + tan^2 θ}

=

{cot^2 θ - tan^2 θ}/{cot^2 θ + tan^2 θ + 2}

=

{(√{11})^2-(1/√{11})^2}/{(√{11})^2+(1/√{11})^2+2}

=

{11-1/{11}}/{11+1/{11}+2}

=

{{121-1}/{11}}/{{121+1+22}/{11}}

=

{120}/{144}

=

5/6

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