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Prove the trigonometric identity. `secx(1+cosx)=1+secx`...

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lkballer24 | Student, Grade 11 | Valedictorian

Posted August 18, 2013 at 11:13 PM via web

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Prove the trigonometric identity.

`secx(1+cosx)=1+secx`

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Mary Joy Ripalda | High School Teacher | (Level 3) Educator

Posted August 19, 2013 at 1:19 AM (Answer #1)

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`secx(1+cosx)=1+secx`

To prove, consider to simplify the left side of the equation. To do so, distribute secx to 1 + cosx.

`secx+secx*cosx=1+secx`

To simplify secx*cosx, take note that secant is reciprocal of cosine `(secx=1/cosx)` .

`secx+1/cosx*cosx=1+secx`

`secx + 1 = 1+secx`

And, apply the commutative property a+b=b+a.

`1+secx=1+secx `     (True)

Since the resulting condition is true, this proves that the given equation is a trigonometric identity.

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