If \cos (2 \theta+54^{\circ})=\sin \theta, 0^{\circ}

SSC CGL 20 Aug 2021 Shift 2 Paper

Question : 70 of 100

Marks: +1, -0

\cos (2 θ+54^{∘})=\sin θ

0^{∘} < (2 θ+54^{∘}) < 90^{∘}

, then what is the value of

\;{1}/{\cot 5 θ+\sec \;{5 θ}/{2}} ?

Solution:

Given,

\cos (2 θ+54^{∘})=\sin θ

⇒ \cos (2 θ+54^{∘})=\cos (90^{∘}-θ)

⇒ \;\; 2 θ+54^{∘}=90^{∘}-θ

⇒ \;\; 3 θ=36^{∘}

⇒ \;\; θ=12^{∘}

∴ \;{1}/{\cot 5 θ+\sec \;{5 θ}/{2}}

=\;{1}/{\cot (5 × 12^{∘})+\sec (\;{5 × 12^{∘}}/{2})}

=\;{1}/{\cot 60^{∘}+\sec 30^{∘}}

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

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