Question

Prove that:
`cospi/10-sinpi/10=sqrt(2)sin(3pi)/(20)`

Answer 1

LHS `=cospi/10-sinpi/10`
`=sin(pi/2-sinpi/10)`
`sin(4pi)/(10)-sinpi/10`
`=2cos((4pi)/(10)+sinpi/10)/(2)sin((4pi)/(10)-pi/10)/(2)`
`=2cospi/4sin(3pi)/20=2(1/sqrt(2))sin(3pi)/(20)`
`=sqrt(2)sin(3pi)/(20)`= RHS Hence Proved.