What is the simplified value of \sqrt{\frac{\cosec A}{\cosec A-1}+\frac{\cosec A}{\cosec A+1}} ?

SSC CGL 10 Aug 2017 Shift 1 Paper

Question : 70 of 100

Marks: +1, -0

What is the simplified value of

√{{\cosec A}/{\cosec A-1}+{\cosec A}/{\cosec A+1}}\ ?

Solution:

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

√{{{\cosec^2 A}+{\cosec A}+{\cosec^2 A}-{\cosec A}}/{{\cosec^2 A-1}}}

√{{2\cosec ^2 A}/{\cot^2}}=√2× {\cosecA}/{\cot A}

=2× 1/{\sin A}× {\sin A}/{\cot A}

=√2× 1/{\cos A}=√2 \sec A

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