Verify the identity

sin^2 (x) cos^2 (x) = 1/8 (1-cos (4x))

Question

Mathematics

Madden Horton

25 July, 23:32

Verify the identity

sin^2 (x) cos^2 (x) = 1/8 (1-cos (4x))

+2

Answers (1)

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Kevin Jimenez · Answer 1

cos^2 (x) = 1/2 + (1/2) cos (2x)

sin^2 (x) = 1 - cos^2 (x) = 1/2 - (1/2) cos (2x)

sin^2 (x) cos^2 (x)

= [1/2 - (1/2) cos (2x) ][1/2 + (1/2) cos (2x) ]

(a - b) (a + b) = a^2 - b^2

= (1/2) ^2 - (1/2) ^2[cos^2 (2x) ]

= 1/4 - (1/4) cos^2 (2x)

= (1/4) [1 - cos^2 (2x) ]

= (1/4) [sin^2 (2x) ]

= (1/4) [1/2 - (1/2) cos (4x) ]

= (1/4) (1/2) [1 - cos (4x) ]

= (1/8) [1 - cos (4x) ]

Verify the identitysin^2 (x) cos^2 (x) = 1/8 (1-cos (4x))

Verify the identity

sin^2 (x) cos^2 (x) = 1/8 (1-cos (4x))