Prove that cos20cos40cos60cos80=1/16
Prove that sin10sin30sin50sin70=1/16
sin10sin30sin50sin70
= 1/2 (sin10sin50sin70)
multiply n divide by 2
= 1/4 ((2sin10sin50) sin70)
= 1/4 ((cos(10-50 ) - cos(10 +50)) sin70)
1/4 ((cos40 - 1/2)sin70)
= 1/4 cos40 sin70 - 1/8 sin70
= 1/8 (2 sin70 cos40) - 1/8 sin70
= 1/8 ( sin110 + sin30 ) -1/8 sin70
= 1/8 ( sin(180-70) +1/2) -1/8 sin70
= 1/8 sin70 + 1/16 - 1/8 sin70
= 1/16