Answer:
Cos 2x = Cos (5x-3x)
Cos(5x)Cos(3x) + Sin(5x)Sin(3x)
Cos 8x = Cos (5x + 3x)
Cos(5x)Cos(3x) - Sin(5x)Sin(3x)
Cos 2x - Cos 8x
= Cos(5x)Cos(3x) + Sin(5x)Sin(3x) -
[Cos(5x)Cos(3x) - Sin(5x)Sin(3x)]
= 2Sin(5x)Sin(3x)
Cos 2x + Cos 8x
= Cos(5x)Cos(3x) + Sin(5x)Sin(3x) +
[Cos(5x)Cos(3x) - Sin(5x)Sin(3x)]
= 2Cos(5x)Cos(3x)
= 2Sin(5x)Sin(3x) ÷ 2Cos(5x)Cos(3x)
2 gets cancelled out
Sin(5x)/Cos(5x) is Tan(5x)
Sin(3x)/Cos(3x) is Tan(3x)
Hence the fraction is identical to
Tan(5x)Tan(3x)
