Question
Mathematics Question on Trigonometric Functions of Sum and Difference of Two Angles
Prove that, cos 6 x = 32cos6 x-48cos4 x+18cos2 x -1.
Answer
L.H.S. = cos 6x
= cos3 (2x)
= 4 cos3 2x - 3 cos 2x [cos 3A = 4 cos3 A - 3 cos A]
= 4 [(2 cos2 x-1)3 -3 (2 cos2 x-1) [cos 2 x = 2 cos2 x-1]
= 4 [(2 cos2 x)3 -(1)3 -3 (2 cos2 x) 2 + 3 (2 cos2 x)]-6cos2 x + 3
= 4 [8 cos6 x-1-12 cos4 x+6 cos2 x]-6 cos2 x+3
= 32 cos6 x- 4 - 48 cos4 x+24 cos2 x-6 cos2 x+3
= 32 cos6 x - 48 cos4 x+18 cos2 x - 1
= R.H.S.