If cosec 39° = x, the value of {1}/{\cosec ^{2} 51^{\^\circ}}+\sin ^{2} 39^{\^\circ}+\tan ^{2} 51^{\^\circ}- {1}/{\sin ^{2} 51^{ ^\circ} \sec ^{2} 39^{\^\circ}} is

SSC CPO SI and ASI 2011 Paper

Question : 142 of 200

Marks: +1, -0

If cosec 39° = x, the value of

{1}/{\cosec ^{2} 51^{\°}}+\sin ^{2} 39^{\°}+

\tan ^{2} 51^{\°}-\ {1}/{\sin ^{2} 51^{ °} \sec ^{2} 39^{\°}}

Solution:

(3)

{1}/{\cosec ^{2} 51^{\°}}+\sin ^{2} 39^{\°}+\tan ^{2} 51^{\°}-

\ {1}/{\sin ^{2} 51^{\°} \sec ^{2} 39^{\°}}

=\sin ^{2}\ (90^{\°}-39^{°}\ )+\sin ^{2} 39^{\°}+\tan ^{2}\(90^{\°}-39^{\°}\ )-

{1}/{\sin ^{2}\(90^{\°}-39^{\°}\ ) \sec ^{2} 39^{\°}}

=\cos ^{2} 39^{°}+\sin ^{2} 39^{\°}+\cot ^{2} 39^{\°} - \ {1}/{\cos ^{2} 39^{\°} \sec ^{2} 39^{\°}}

=1+\cot ^{2} 39^{\°}-1

=\cosec ^{2} 39^{\°}-1=\ {x}^{2}-1

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