RRB Assistant Loco Pilot and Technician Model Paper 10 with solutions

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Question : 16 of 75

Marks: +1, -0

{\cosec \A }/{\cosec \A – 1}

+

{\cosec \A} /{\cosec \A + 1}

is equal to

1
$\sec^2$ A
$\cosec^2$ A
2 $\sec^2$ A

Solution:

{\cosec \A }/{\cosec \A – 1}

+

{\cosec \A} /{\cosec \A + 1}

⇒

{\cosec A(\cosecA +1) + \cosec A(\cosec A –1)}/{\cosec^2 \A – 1 }

⇒

{\cosec^2 A + \cosec A + \cosec^2 A – \cosecA}/{\cosec^2 \A – 1 }

⇒

{2\cosec^2 A}/{\cosec^2 \A – 1 }

⇒

{2\cosec^2 A}/{\cot^2 A}

⇒

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

⇒

{2\cosec^2 A⋅{\sin^2 A}}/{{\cos^2 A}}

⇒

{2\cosec^2 A⋅{1/{\cosec^2 A}}}/{{\cos^2 A}}

⇒

2/{\cos^2 A}

= 2

\sec^2

A

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