Trigo: show 1/(2 sin(2pi/5)) = (2cos^2(pi/5) - 1)/(sin(pi/5))

[SKY KEUNG]

I wonder how to solve 35(b)(ii).
I tried and here is my work.
The photo may not be clear enough. ABC is an isosceles triangle in which AB=AC,angle BAC=pi/5 rad.and BD bisects angle ABC.

 

[SKY KEUNG]

Cos(pi/5)=?

HEY,ME,AGAIN.
I CAN DO b(ii) but i can't do part c
I think i should make a quadratic equation about cos(pi/5).

 

[Deleted member 4993]

HEY,ME,AGAIN.
I CAN DO b(ii) but i can't do part c
I think i should make a quadratic equation about cos(pi/5).View attachment 8314View attachment 8313

Have you thought of using:

sin(2π/5) = 2 * sin(π/5) * cos(π/5)