Evaluate the following expression. {3(\cot ^{2} 46^{\circ}-\sec ^{2} 44^{\circ})}/{2(\sin ^{2} 28^{\circ}+\sin ^{2} 62^{\circ})} + {2 \cos ^{2} 60^{\circ} \tan ^{2} 33^{\circ} \tan ^{2} 57^{\circ}}/{\sec ^{2}(90^{\circ}-\theta)-\cot ^{2} \theta}

SSC CHSL 10 Aug 2021 Shift 1 Paper

Section: Quantitative Aptitude

Question : 56 of 100

Marks: +1, -0

Evaluate the following expression.

\;{3(\cot ^{2} 46^{∘}-\sec ^{2} 44^{∘})}/{2(\sin ^{2} 28^{∘}+\sin ^{2} 62^{∘})}

+\;{2 \cos ^{2} 60^{∘} \tan ^{2} 33^{∘} \tan ^{2} 57^{∘}}/{\sec ^{2}(90^{∘}-θ)-\cot ^{2} θ}

Solution:

Given,

\;\;{3(\cot ^{2} 46^{∘}-\sec ^{2} 44^{∘})}/{2(\sin ^{2} 28^{∘}+\sin ^{2} 62^{∘})}

+ \;{2 \cos ^{2} 60^{∘} \tan ^{2} 33^{∘} \tan ^{2} 57^{∘}}/{\sec ^{2}(90^{∘}-θ)-\cot ^{2} θ}

=\;{3[\cot ^{2}(90^{∘}-44^{∘})-\sec ^{2} 44^{∘}]}/{2[\sin ^{2}(90^{∘}-62^{∘})+\sin ^{2} 62^{∘}]}

+\;{2 \cos ^{2} 60^{∘} × \tan ^{2}(90^{∘}-57^{∘}) × \tan ^{2} 57^{∘}}/{cosec^{2} θ-\cot ^{2} θ}

=\;{3(\tan ^{2} 44^{∘}-\sec ^{2} 44^{∘})}/{2(\cos ^{2} 62^{∘}+\sin ^{2} 62^{∘})}

+\;{2 \cos ^{2} 60^{∘} × \cot ^{2} 57^{∘} × \tan ^{2} 57^{∘}}/{1}

=\;{3 ×(-1)}/{2 × 1}+\;{2 \cos ^{2} 60^{∘} × 1}/{1}

=\;{-3}/{2}+2 ×(\;{1}/{2})^{2}=\;{-3}/{2}+\;{1}/{2}

=\;{-3+1}/{2}=\;{-2}/{2}=-1

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