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verify the identity : `cos 4t = 1 - 8*sin^2t*cos^2t`

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eromero8907 | Student | eNotes Newbie

Posted February 27, 2012 at 3:50 PM via web

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verify the identity : `cos 4t = 1 - 8*sin^2t*cos^2t`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 27, 2012 at 4:38 PM (Answer #1)

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The identity `cos 4t = 1 - 8*sin^2t*cos^2t` has to be verified.

`cos 4t = cos(2*2t)`

Use the formula `cos 2t = 1 - 2*sin^2 t`

=> `1 - 2*sin^2(2t)`

Use the formula `sin 2t = 2*sin t*cos t`

=> `1 - 2*(2*sin t*cos t)^2`

=> `1 - 2*4*sin^2t*cos^2t`

=> `1 - 8*sin^2t*cos^2t`

This proves that `cos 4t = 1 - 8*sin^2t*cos^2t`

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lochana2500 | TA , Undergraduate | (Level 1) Valedictorian

Posted June 29, 2012 at 3:26 PM (Answer #2)

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L:H:S = cos4t

= 1-2sin²2t

= 1-2(2sint.cost)²

= 1-2(4sin²t.cos²t)

= 1-8sin²t.cos²t

= R:H:S

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