If \cos \theta=\frac\sqrt{3}{2}, then the value of {2-\sin ^{2} \theta}/{1-\cot ^{2} \theta}+(\sec ^{2} \theta+cosec \theta) is

SSC CHSL 5 Aug 2021 Shift 3 Paper

Section: Quantitative Aptitude

Question : 69 of 100

Marks: +1, -0

\cos θ=\;{√{3}}/{2}

, then the value of

\;{2-\sin ^{2} θ}/{1-\cot ^{2} θ}+(\sec ^{2} θ+cosec θ)

Solution:

Given,

\cos θ=\;{√{3}}/{2}=\cos 30^{∘}

∴ \;\; θ=30^{∘}

Then the value of

\;{2-\sin ^{2} θ}/{1-\cot ^{2} θ}+(\sec ^{2} θ+cosec θ)

\;\; =\;{2-\sin ^{2} 30^{∘}}/{1-\cot ^{2} 30^{∘}}+(\sec ^{2} 30^{∘}+cosec 30^{∘})

\;\; =\;{2-{1}/{4}}/{1-3}+(\;{4}/{3}+2)=\;{7}/{4} ×(\;{1}/{-2})+\;{10}/{3}

=\;{10}/{3}-\;{7}/{8}

=\;{80-21}/{24}=\;{59}/{24}

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