Question

Simplify the expression please.

Answer 1

Answer:

tanx·secx

Step-by-step explanation:

To simply this, you can begin by factoring sin x out of the numerator to become:

$\frac{sinx (sin^{2}x +cos^{2} x)}{cos^{2} x}$

Now, using Pythagorean Trig Identities, we know that sin²x+cos²x equals 1. We can substitute this to make the equation become:

$\frac{sinx}{cos^{2}x }$

First of all, we can convert $\frac{sinx}{cosx}$ to tanx. However, we have a remaining $\frac{1}{cosx}$ which, using reciprocal identities, will become sec x.

Finally, we get our answer as tanx·secx.