Question

If Cosec θ = 17/8, then Cot θ = ?

A) 17/8 B) 15/8 C) 8/15 D) 17/15

Answer 1

$Given \: Cosec \theta = \frac{17}{8} \: --(1)$

$\red { Value \: of \: Cot \theta } \\= \sqrt{ Cosec^{2} \theta - 1 } \\= \sqrt{ (\frac{17}{8})^{2} - 1 } \\= \sqrt{ \frac{ 289}{64} - 1 } \\= \sqrt{ \frac{ 289 - 64 }{ 64}} \\= \sqrt{ \frac{225}{64}} \\= \sqrt{(\frac{15}{8})^{2}} \\= \frac{15}{8}$

Therefore.,

$\red { Value \: of \: Cot \theta }\green {= \frac{15}{8}}$

$Option \:\pink { ( C ) } \: is \: correct.$

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