cos 6x = 32 cos⁶ x – 48 cos⁴ x + 18 cos² x – 1

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Solution

L.H.S. = cos 6x

= cos 3(2x)

= 4 cos³ 2x – 3 cos2x

= 4 [2 cos² x – 1)³ – 3 (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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Similar questions

cos 6 x = 32 {cos}^{6} x - 48 {cos}^{4} x + 18 {cos}^{2} x - 1

cos 6 x = 32 {cos}^{6} x - 48 {cos}^{4} x + 18 {cos}^{2} x - 1

c o s 6 x = 32 c o s^{6} x - 48 c o s^{4} x + 18 c o s^{2} x - 1

cos 6 x = 32 {cos}^{6} x - 48 {cos}^{4} x + 18 {cos}^{2} x - m

m

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