Ex 3.3, 25 - Chapter 3 Class 11 Trigonometric Functions

Last updated at August 14, 2026 by

Ex 3.3, 25 - Prove cos 6x = 32 cos6 x - 48 cos4 x + 18 cos2x - Ex 3.3

part 2 - Ex 3.3, 25 - Ex 3.3 - Serial order wise - Chapter 3 Class 11 Trigonometric Functions

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Transcript

Ex 3.3, 25 Prove that: cos 6๐‘ฅ = 32 cos6 ๐‘ฅ โ€“ 48 cos4 ๐‘ฅ + 18 cos2 ๐‘ฅ โ€“ 1 Solving L.H.S. cos 6x = 2(cos 3x)2 โ€“ 1 = 2 ( 4 cos3 x โ€“ 3 cos x)2 โ€“ 1 We know that cos 2x = 2 cos2 x โ€“ 1 Replacing by 3x cos 2(3x) = 2 cos2 (3x) -1 cos 6x = 2 cos2 3x -1 Using (a โ€“ b)2 = a2 + b2 โ€“ 2ab = 2 [(4 cos3 x)2 + (3 cos x )2 โ€“ 2 (4 cos3 x) ร— (3 cos x)] โ€“ 1 = 2 [(16 cos6x + 9 cos2 x โ€“ 24 cos4x)] โ€“ 1 = 2 ร— 16 cos6x + 2 ร— 9 cos2 x โ€“ 2 ร— 24 cos4x โ€“ 1 = 32 cos6x โ€“ 48 cos4x + 18 cos2x โ€“ 1 = R.H.S. Hence L.H.S. = R.H.S Hence proved

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