Question 25:
Prove that: cos 6x = 32 cos6 x − 48 cos4 x + 18 cos2 x – 1
Answer
L.H.S. = cos 6x
= cos 3(2x)
= 4 cos3 2x − 3 cos2x [cos 3A = 4 cos3 A − 3 cosA]
= 4 [(2 cos2 x − 1)3 − 3 (2 cos2 x − 1) [cos 2x = 2 cos2 x − 1]
= 4 [(2 cos2 x)3 − (1)3 − 3 (2 cos2 x)2 + 3 (2 cos2 x)] − 6cos2 x + 3
= 4 [8cos6x − 1 − 12 cos4x + 6 cos2x] − 6 cos2x + 3
= 32 cos6x − 4 − 48 cos4x + 24 cos2 x − 6 cos2x + 3
= 32 cos6x − 48 cos4x + 18 cos2x – 1
= R.H.S.
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