Question

If tan 9 theta = cot theta then find the value of cosec5

Answer 1

tan 9 a= cot a
tan 9a=tan (90 -a)
9a=90-a
10a=90
a=9
cosec 5×9
cosec 45
√2

Answer 2

Answer:

$cosec\:5\theta = \sqrt{2}$

Step-by-step explanation:

$Given \:tan\:9\theta = cot \theta$

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

/* Since , Cot A = tan(90-A) */

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

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

$\implies 10\theta = 90$

$\implies \theta = \frac{90}{10}=9$

$Now, \\cosec5\theta \\=cosec\: (5\times 9)\\=cosec\:45\degree\\=\sqrt{2}$

Therefore,

$cosec\:5\theta = \sqrt{2}$

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