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Prove that `1/(sec^2x) = sin^2x*cos^2x + cos^4x`

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xetaalpha | Student | Honors

Posted June 5, 2012 at 4:12 PM via web

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Prove that `1/(sec^2x) = sin^2x*cos^2x + cos^4x`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 5, 2012 at 4:17 PM (Answer #1)

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The identity `1/(sec^2x) = sin^2x*cos^2x + cos^4x` has to be proved.

`sin^2x*cos^2x + cos^4x`

=> `(1 - cos^2x)*cos^2x + cos^4x`

=> `cos^2x - cos^4x + cos^4x`

=> `cos^2x`

=> `1/(sec^2x)`

This proves that `1/(sec^2x) = sin^2x*cos^2x + cos^4x`

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lochana2500 | Student , Undergraduate | Valedictorian

Posted June 29, 2012 at 4:08 PM (Answer #2)

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R:H:S = sin²x.cos²x + cos⁴x

= cos²x(sin²x+cos²x)

we know that sin²x+cos²x=1

=cos²x

= 1/sec²x

 

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