Question

tan(2π /18) × tan(4π /18) × tan(8π / 18) =

Answer 1

tan (2Π/18) × tan(4Π/18)×tan(8Π/18)

Take common tan (2Π/18)

tan(2Π/18) { 1×2Π×4Π}

tan (2Π/18)(8Π)

tan16Π/18

Answer 2

Answer:

$\large\boxed{\tan(\frac{\pi }{9})\tan (\frac{2\pi }{9})\tan (\frac{4\pi }{9})=1.73}$

Step-by-step explanation:

To solve this problem, first you have to use pie or tan formula from left to right.

Given:

tan(2π /18) × tan(4π /18) × tan(8π / 18

Solutions:

First, multiply.

$\displaystyle 2*\frac{\pi}{18}$

Common factor of 2.

$\displaystyle 18\div2=9$

$\displaystyle \frac{\pi}{9}$

Next, multiply numbers from left to right.

$\displaystyle 4*\frac{\pi}{18}$

Common factor of 2.

$\displaystyle 4\div2=2\quad 18\div2=9$

$\displaystyle \frac{2\pi}{9}$

$\displaystyle\tan (\frac{\pi }{9})\tan (\frac{2\pi }{9})\tan (8*\frac{\pi }{18})$

Solve.

Multiply.

$\displaystyle 8*\frac{\pi}{18}$

$\displaystyle \frac{\pi8}{18}$

Common factor of 2.

Divide numbers from left to right.

$\displaystyle 8\div2=4\quad18\div2=9$

$\displaystyle\tan \left(\frac{\pi }{9}\right)\tan \left(\frac{2\pi }{9}\right)\tan \left(\frac{4\pi }{9}\right)$

$\large\boxed{\tan \left(\frac{\pi }{9}\right)\tan \left(\frac{2\pi }{9}\right)\tan \left(\frac{4\pi }{9}\right)}$

In conclusion, the correct answer is tan(π/9)tan(2π/9)tan(4π/9).