Simplifying $\frac{\sin x+\sin x\tan^2x}{\tan x}$ to $\sec x$ 
I have to simplify (the answer is $\sec(x)$):
$$\frac{\sin(x)+\sin(x)\cdot\tan^2(x)}{\tan(x)}$$

I have looked at images for all trig identities but nothing shows $\sin(x)+\sin(x)$ or $\frac{\sin\left(x\right)+\sin\left(x\right)}{\tan\left(x\right)}$
In short: I tried brute tests on the calculator, but different values give differing answers.
Longer explanation: I tried to test random values (but the same value for each function), and keep getting differing results. Such as $\tan(45)^2 = 1$ in degree mode, but $\tan(5)^2 != 1$. Tried in Radian mode and the results are $2.62$ and $11.43$ respectively. So couldn't pick out a pattern.
**EDIT
Thank you for those who have provided answers. I really can not figure out what happened to my original $sin(x) + $ in all the answers provided.
 A: Using $$1 + \tan^{2}(x) = \frac{\cos^{2}(x) + \sin^{2}(x)}{\cos^{2}(x)} = \frac{1}{\cos^{2}(x)}$$ then $$\frac{\sin(x) \, (1 + \tan^{2}(x))}{\tan(x)} = \frac{\sin(x)}{\cos^{2}(x) \, \tan(x)} = \frac{1}{\cos(x)}.$$
A: In these types of questions, the general method is to convert the expression into sines and cosines. Letting $s=\sin x,c=\cos x$,  we get $$\begin{split}\frac{\sin(x)+\sin(x)\tan(x)^2}{\tan(x)}&=\frac{s+s(s/c)^2}{s/c}\\&=\frac{sc^2+s^3}{sc}\\&=\frac{s^2+c^2}{c}\\&=\frac1c=\sec(x)\end{split}$$
where we used that $\tan(x)=\sin(x)/\cos(x)=s/c$, and $\sin(x)^2+\cos(x)^2=1$, i.e. $s^2+c^2=1$.
A: This is equivalent to $$\frac{\sin x}{\tan x} + \sin x \tan x = \cos x + \frac{\sin^2x}{\cos x} = \cos x + \frac{(1-\cos^2x)}{\cos x} = \frac{1}{\cos x}.$$ Or, you can use it is equivalent to $$\frac{\sin x (1+\tan^2x)}{\tan x} = \frac{(\sin x \frac{1}{\cos^2x})}{\tan x} = \frac{\cos x }{\cos^2x} = \frac{1}{\cos x}.$$
A: This question is easily solve by factoring and knowing that $1+\tan^2{x}=\sec^2x$
$$\frac{\sin x+\sin x \tan^2x}{\tan x}=\frac{\sin x (1+\tan^2x)}{\tan x}$$
$$\frac{\sin x \sec^2x}{\tan x}=\frac{\tan x \sec x}{\tan x}=\sec x=\boxed{\frac{1}{\cos x}}$$
In almost any mathematics excersise you should factorize whenever you can, it gives you a wider view of the problem and it can make it easier. Even when computing basic algebra calculations such as division, factorizing can be the key to solving them quickly and flawless
