Prove that cos 6x = 32 cos6 x- 48 cos4 x + 18 cos2 x- 1.
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Prove that cos 6x = 32 cos6 x- 48 cos4 x + 18 cos2 x- 1.
Prove that cos 6x = 32 cos6 x- 48 cos4 x + 18 cos2 x- 1.
L.H.S. = cos 6x = cos 3(2x) [∵ cos 3x = 4 cos3 x – 3 cos x]
= 4 cos3 2x – 3 cos 2x
= cos 2x (4 cos2 2x – 3)
= cos 2x [4(cos 2x)2 – 3] [∵ cos 2x = 2 cos2 x – 1]
= cos 2x [4(2 cos2 x – l)2 – 3]
= cos 2x [4(4 cos4 x + 1 – 4 cos2 x) – 3]
= cos 2x (16 cos4 x + 4 – 16 cos2 x – 3)
= (2 cos2 x – 1) (16 cos4 x + 4 – 16 cos2 x – 3)
= 32 cos6 x + 8 cos2 x – 32 cos4 x – 6 cos2 x – 16 cos4 x – 4 + 16 cos2 x + 3
= 32 cos6 x – 48 cos4 x + 18 cos2 x – 1
= R.H.S. Hence Proved.