Prove that cos² 2x – cos² 6x = sin 4x sin 8x

Open in App

Solution

It is known that

∴L.H.S. = cos² 2x – cos² 6x

= (cos 2x + cos 6x) (cos 2x – 6x)

= [2 cos 4x cos 2x] [–2 sin 4x (–sin 2x)]

= (2 sin 4x cos 4x) (2 sin 2x cos 2x)

= sin 8x sin 4x

= R.H.S.

Suggest Corrections

185

Similar questions

{cos}^{2} 2 x - {cos}^{2} 6 x = sin 4 x sin 8 x

Cos²2x-cos²6x=sin4x sin8x

{cos}^{2} 2 x - {cos}^{2} 6 x = sin m x sin 8 x

m

1 + {cos}^{2} 2 x = 2 ({cos}^{4} x + {sin}^{4} x)

1 + {cos}^{2} 2 x = 2 ({cos}^{4} x + {sin}^{4} x)

Join BYJU'S Learning Program