Answer:
tanx·secx
Step-by-step explanation:
To simply this, you can begin by factoring sin x out of the numerator to become:
[tex]\frac{sinx (sin^{2}x +cos^{2} x)}{cos^{2} x}[/tex]
Now, using Pythagorean Trig Identities, we know that sin²x+cos²x equals 1. We can substitute this to make the equation become:
[tex]\frac{sinx}{cos^{2}x }[/tex]
First of all, we can convert [tex]\frac{sinx}{cosx}[/tex] to tanx. However, we have a remaining [tex]\frac{1}{cosx}[/tex] which, using reciprocal identities, will become sec x.
Finally, we get our answer as tanx·secx.
