[Tan x/csc^2 x] + [Tan x/ sec^2 x] I am suppose to turn these into sin and cosine and then simplify to get tan x, any help on how to solve this problem would be great thanks for the help.
Hello, algebraisabeast!
What did you try?
$\displaystyle \frac{\tan x}{\csc^2\!x} + \frac{\tan x}{\sec^2\!x} \:=\:\tan x$
$\displaystyle \frac{\tan x}{\csc^2\!x} + \frac{\tan x}{\sec^2\!x} \;=\;\tan x\left(\frac{1}{\csc^2\!x} + \frac{1}{\sec^2\!x}\right) \;=\;\tan x\underbrace{\left(\sin^2\!x + \cos^2\!x\right)}_{\text{This is 1}} \;=\;\tan x $