Find the value of \frac{3}{4} \cot ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}-3 cosec^{2} 60^{\circ} +\tan ^{2} 60^{\circ}.

SSC CGL 17 Aug 2021 Shift 1 Paper

Question : 59 of 100

Marks: +1, -0

Find the value of

\;{3}/{4} \cot ^{2} 30^{∘}+\cos ^{2} 30^{∘}-3 cosec^{2} 60^{∘}

+\tan ^{2} 60^{∘}

Solution:

\;{3}/{4} \cot ^{2} 30^{∘}+\cos ^{2} 30^{∘}

\;\; -3 cosec^{2} 60^{∘}+\tan ^{2} 60^{∘}

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

+(√{3})^{2}

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

= \;\; \;{9}/{4}+\;{3}/{4}-1=\;{(12-4)}/{4}=\;{8}/{4}=2 .

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