Question #f8c0c

1 Answer
May 25, 2017

#1/α#

Explanation:

The key here is to know that:
#cos(x)=sin(pi/2-x)#

Given:
#sec((4pi)/9)=α#

Then:
#cos((4pi)/9)=sin(pi/2-(4pi)/9)#
#cos((4pi)/9)=sin((9pi-8pi)/18)#
#cos((4pi)/9)=sin(pi/18)#

Since these two functions are equal it is only a matter of finding the secant equivalent.

#[cos((4pi)/9)=sin(pi/18)]^-1#
#sec((4pi)/9)=1/(sin(pi/18))#
#α=1/(sin(pi/18))#
#sin(pi/18)=1/a#