Question

if tan theta=8/15 and theta is acute then cosec theta=?

Answer 1

$Given \:tan \theta = \frac{8}{15} \:---(1)$

$\implies cot\theta = \frac{1}{tan \theta} \\= \frac{1}{\frac{8}{15}} \\= \frac{15}{8} \: --(2)$

$We \:know \:the \: Trigonometric \: identity: \\\boxed {\pink { cosec^{2} \theta = 1 + cot^{2} \theta }}$

$cosec^{2} \theta = 1 + \Big( \frac{15}{8}\Big)^{2} \\= 1 + \frac{225}{64} \\= \frac{64+225}{64} \\= \frac{289}{64} \\= \Big(\frac{17^{2}}{8^{2}}\Big)\\= \Big(\frac{17}{8}\Big)^{2}$

$\implies Cosec \theta = \sqrt{ \Big(\frac{17}{8}\Big)^{2}}\\= \frac{17}{8}$

Therefore.,

$\red {Value \:of \:Cosec \theta }\green{=\frac{17}{8}}$

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Answer 2

Referred to the attachments........