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Verify: tan^2x - sin^2x= (tan^2x)(sin^2x)

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lek123 | Student, Grade 11 | eNotes Newbie

Posted March 13, 2010 at 5:58 AM via web

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Verify:

tan^2x - sin^2x= (tan^2x)(sin^2x)

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neela | High School Teacher | Valedictorian

Posted March 13, 2010 at 10:34 AM (Answer #1)

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We know the sin^2+cos^x = 1.

Therefore sin^2x = 1-cos^2x.

Tanx = sinx/cosx. We use these identities in the course of the solution.

 

RHS:  tan^2 x  * sin^2x = tan^2x (1-cos^2x),

=tan^2x-(tan^2x)*cosx^2.

=tan^2x-(sinx/cosx)^2*cos^2x.

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

=tan^2x - sin^2x*cos^2x/cos^2x

=tan^2x - sin^2 x  which is LHS.

 

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lochana2500 | Student, Undergraduate | Valedictorian

Posted June 22, 2012 at 4:31 PM (Answer #2)

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R:H:S ≡ tan²x.sin²x

= tan²x(1-cos²x)

= tan²x - tan²x.cos²x

= tan²x - (sin²x/cos²x)*cos²x

= tan²x - sin²x

=R:H:S 

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anthonda49 | Middle School Teacher | (Level 2) Associate Educator

Posted March 13, 2010 at 8:37 AM (Answer #3)

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tan^2x - sin^2x =

tan^2x(1-cos^2x) =

(tan^2x)(sin^2x)

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