Question

How do you use a double angle formula to write 1-2sin^2(pi/5) as a single trig function of twice the angle?

Answer 1

`=cos((2pi)/5)`

Explanation:

.

`1-2sin^2(pi/5)`

`sin^2x=1/2(1-cos2x)`

`sin^2(pi/5)=1/2(1-cos((2pi)/5))`

`1-2sin^2(pi/5)=1-2(1/2)(1-cos((2pi)/5))=1-1+cos((2pi)/5)=cos((2pi)/5)`