Question

How do you show that `sin(pi/5)+cos(pi/5)=sin((3pi)/10)+cos((3pi)/10)`?

Answer 1

`LHS=sin(pi/5)+cos(pi/5)`

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

`=cos((5pi-2pi)/10)+sin((5pi-2pi)/10)`

`=cos((3pi)/10)+sin((3pi)/10)=RHS`