What is the value of \sin ^{2} 60^{\circ}+\tan ^{2} 45^{\circ}+\sec ^{2} 45^{\circ}-cosec^{2} 30^{\circ} ?

SSC CHSL 12 Apr 2021 Shift 2 Paper

Section: Quantitative Aptitude

Question : 63 of 100

Marks: +1, -0

What is the value of

\sin ^{2} 60^{∘}+\tan ^{2}

45^{∘}+\sec ^{2} 45^{∘}-cosec^{2} 30^{∘} ?

Solution:

Given,

\sin ^{2} 60^{∘}+\tan ^{2} 45^{∘}

+\sec ^{2} 45^{∘}-cosec^{2} 30^{∘}

Putting the values,

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

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

\;\; =\;{3+4+8-16}/{4}=-\;{1}/{4}

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