1+ctg²(π/5) = 2*cos12°*cos48° = Sin40°-Sin18° =

Question

1+ctg²(π/5) =
2*cos12°*cos48° =
Sin40°-Sin18° =

Answer 1

1+ctg²(π/5)=1/sin²(π/5)
2cos12*cos48=2*1/2(cos12-48)+cos(12+48))=cos36+cos60=cos36+1/2
sin40-sin18=2sin(40-18)/2*cos(40+18)/2=2sin22*cos29