Question

if tan 9 theta is equal to COT theta and 9 theta is less than 90 degree then find the value of cosec 5 theta

Answer 1

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Answer 2

Answer:

$</p><p>value \: of \: cosec\: 5\theta = \sqrt{2}$

Step-by-step explanation:

$Given \: tan 9\theta = cot \theta \: and \: 9\theta < 90\degree$

$\implies tan 9\theta = tan(90-\theta)$

$we \: know \: that ,\boxed {cot\theta = tan(90-\theta)}$

$\implies 9\theta = 90 - \theta$

$\implies 9\theta + \theta = 90\degree$

$\implies 10\theta = 90\degree$

$\implies \theta = \frac{90}{10}$

$\implies \theta =9\degree\:---(1)$

$Now, value \: of \: cosec\: 5\theta \\=cosec\: 5 \times 9\degree \:[ from \:(1) ]$

$= cosec\: 45\degree\\=\sqrt{2}$

Therefore.,

$</p><p>value \: of \: cosec\: 5\theta = \sqrt{2}$

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