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Topic: Math Verify: (cos^2x)(tan^2x) + (cos^2x)= 1 Thank you in advance....

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luisrobertofl... | eNotes Newbie

Posted June 11, 2013 at 5:53 PM via web

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Topic: Math

Verify: (cos^2x)(tan^2x) + (cos^2x)= 1


Thank you in advance....

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted June 11, 2013 at 6:09 PM (Answer #1)

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In trigonometry there is a major trigonometric identity as;

`sin^2x+cos^2x = 1`

 

We also know that;

`tanx = (sinx)/cosx`

 

Now we will start the question from Left Hand Side(LHS)

`LHS`

`= (cos^2x)tan^2x+cos^2x`

`= (cos^2x)(sin^2x)/(cos^2x)+cos^2x`

`= sin^2x+cos^2x`

`= 1`

`= RHS`

 

So it is proven that `(cos^2x)tan^2x+cos^2x = 1`

 

Sources:

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted June 11, 2013 at 6:21 PM (Answer #2)

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Show `cos^2x(tan^2x)+cos^2x=1` :

`cos^2x(tan^2x)+cos^2x`   Given

`=cos^2x(tan^2x+1)`  Factor out common term

`=cos^2x(sec^2x)` Pythasgorean relationship

`=cos^2x*1/(cos^2x)`  Definition of sec(x)

`=1` as required.

 

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