SSC CGL Model Paper 7

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Question : 69 of 100

Marks: +1, -0

If

1/{\cosecθ+\cotθ}-\cosecθ-\tanθ

= 5k.\secθ.\cosecθ

, then value of k ?

$1/5$
$-1/2$
$1/3$
$-1/5$

Solution:

1/{\cosecθ+\cotθ}-\cosecθ-\tanθ

({\cosecθ-\cotθ})/{({\cosecθ+\cotθ})({\cosecθ-\cotθ})}

-\cosecθ-\tanθ

=

{\cosecθ-\cotθ}/{\cosec^2θ-\cot^2θ}-\cosecθ-\tanθ

=

\cosecθ-\cotθ-\cosecθ-\tanθ

=

-({\cosθ}/{\sinθ}+{\sinθ}/{\cosθ})=-({\cos^2θ+\sin^2θ}/{\sinθ.\cosθ})

⇒

-\cosecθ.\secθ== 5k.\secθ.\cosecθ

∴

5k = -1 ⇒ k=-1/5

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