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

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lemjay eNotes educator| Certified Educator


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


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


`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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