# Prove the trigonometric identity. `secx(1+cosx)=1+secx` http://postimg.org/image/jgxhkg1nb/

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lemjay | Certified Educator

`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.**