Evaluate the following expression {\tan ^{2} 60^{\circ}+cosec 30^{\circ} \sin 90^{\circ}+3 \sec ^{2} 30^{\circ}}/{4 \sin ^{2} 45^{\circ}+\sec ^{2} 60^{\circ}-\cot ^{2} 30^{\circ}-5 \cos ^{2} 90^{\circ}}

SSC CHSL 6 Aug 2021 Shift 1 Paper

Section: Quantitative Aptitude

Question : 69 of 100

Marks: +1, -0

Evaluate the following expression

\;{\tan ^{2} 60^{∘}+cosec 30^{∘} \sin 90^{∘}+3 \sec ^{2} 30^{∘}}/{4 \sin ^{2} 45^{∘}+\sec ^{2} 60^{∘}-\cot ^{2} 30^{∘}-5 \cos ^{2} 90^{∘}}

Solution:

Given,

\;{\tan ^{2} 60^{∘}+cosec 30^{∘} \sin 90^{∘}+3 \sec ^{2} 30^{∘}}/{4 \sin ^{2} 45^{∘}+\sec ^{2} 60^{∘}-\cot ^{2} 30^{∘}-5 \cos ^{2} 90^{∘}}

Putting all trigonometric value and solving it,

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

4 ×(\;{1}/{√{2}})^{2}+(2)^{2}-(√{3})^{2}-5 ×(0)^{2}

=\;{3+2+4}/{2+4-3}=\;{9}/{3}=3

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