SSC CHSL 17 Mar 2020 Shift 3 Paper

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Question : 69 of 100

Marks: +1, -0

If

\cot \θ={80}/{39}

, find the value of

{\cosec} \θ

.

${39}/{80}$
${89}/{39}$
${39}/{89}$
${89}/{80}$

Solution:

We know that,

{\cosec}^{2} \θ-\cot ^{2} \θ=1

⇒

{\cosec}^{2} \θ=1+\cot ^{2} \θ

⇒

{\cosec}^{2} \θ=1+({80}/{39})^{2}

(\∵\cot \θ={80}/{39}.

, given

)

⇒

{\cosec}^{2} \θ=1+{6400}/{1521}

⇒

{\cosec}^{2} \θ={1521+6400}/{1521}

⇒

{\cosec}^{2} \θ={7921}/{1521}

∴

{\cosec} \θ={89}/{39}

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