Find the value of {\tan ^{2} 30^{\circ}}/{\sec ^{2} 30^{\circ}}+ {cosec^{2} 45^{\circ}}/{\cot ^{2} 45^{\circ}}- {\sec ^{2} 60^{\circ}}/{cosec^{2} 60^{\circ}}

SSC CGL 23 Aug 2021 Shift 1 Paper

Question : 59 of 100

Marks: +1, -0

Find the value of

\;{\tan ^{2} 30^{∘}}/{\sec ^{2} 30^{∘}}+\;{cosec^{2} 45^{∘}}/{\cot ^{2} 45^{∘}}-\;{\sec ^{2} 60^{∘}}/{cosec^{2} 60^{∘}}

Solution:

Given expression,

\;{\tan ^{2} 30^{∘}}/{\sec ^{2} 30^{∘}}+\;{cosec^{2} 45^{∘}}/{\cot ^{2} 45^{∘}}-\;{\sec ^{2} 60^{∘}}/{cosec^{2} 60^{∘}}

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

=\;{({1}/{3})}/{2 × \;{2}/{3}}+\;{2}/{1}-\;{4}/{{4}/{3}}

=\;{1}/{4}+2-3

=\;{1}/{4}-1=-\;{3}/{4}

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