Question

Find the value of cot pi/20 . cot3pi/20 . cot 5pi/20 . cot 7pi/20 . cot 9pi/20

Answer 1

Answer:

Is 1

Step-by-step explanation:

The answer is given below

Hope it might help u

Answer 2

The value is $1$

The given trigonometry equation is

$cot \frac{\pi }{20} . cot \frac{3\pi }{20} .cot \frac{5\pi }{20} .cot \frac{7\pi }{20} .cot \frac{9\pi }{20}$

Find the value of given trigonometry equation is

$cot \frac{\pi }{20} . cot \frac{3\pi }{20} .cot \frac{5\pi }{20} .cot \frac{7\pi }{20} .cot \frac{9\pi }{20}$

First, convert $cot\frac{7\pi }{20} .cot\frac{9\pi }{20} .cot\frac{15\pi }{20}$ in terms of tan.

$cot\frac{9\pi }{20}=tan(\frac{\pi }{2}-\frac{9\pi }{20} ) =tan \frac{\pi }{20}$

$cot\frac{9\pi }{20}=tan(\frac{\pi }{2}-\frac{15\pi }{20} ) =tan \frac{5\pi }{20}$

$and \frac{1}{cot \theta} =tan \theta$

$cot\frac{\pi }{20}. cot\frac{3\pi }{20}.cot\frac{5\pi }{20} .tan\frac{3\pi }{20}.tan\frac{\pi }{20}.tan\frac{5\pi }{20}$

$cot\frac{\pi }{20}. cot\frac{3\pi }{20}.cot\frac{5\pi }{20} .\frac{1}{cot\frac{3\pi }{20}} .\frac{1}{cot\frac{\pi }{20}}.\frac{1}{cot\frac{5\pi }{20}}$

$=1$

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