I'm supposed to prove the question in the attachment.....
Ive done some steps, but still cannot solve it
To be fair Plato, at least the OP has shown some working and is asking for some guidance in the spot where stuck. That is more than most people asking questions do.
As for the OP, there are a few things you could do to ensure you get more help quicker. First, if you MUST handwrite, please do so legibly. Better, learn some LaTeX, as the site has an inbuilt compiler. The LaTeX sub-forum is a good place to start. It also helps to post your pictures the right way up, as we are unable to rotate them and I find it difficult holding my laptop on an angle or upside down to read them.
Hello, Thorpelizts!
I found a "magic step" which facilitates the proof: .$\displaystyle 1 \;=\;\sin^2\!A + \cos^2\!A$ .[1]
$\displaystyle \text{Prove: }\:\frac{2-\csc^2\!A}{\csc^2\!A + 2\cot A} \;=\;\frac{\sin A - \cos A}{\sin A + \cos A}$
The left side is: .$\displaystyle \dfrac{2-\dfrac{1}{\sin^2\!A}}{\dfrac{1}{\sin^2\!A} + \dfrac{2\cos A}{\sin A}} $
Multiply by $\displaystyle \tfrac{\sin^2\!A}{\sin^2\!A}\!:\;\;\frac{2\sin^2\! A - 1}{1 + 2\sin A\cos A}$
Substitute [1]: .$\displaystyle \dfrac{2\sin^2\!A - (\sin^2\!A + \cos^2\!A)}{(\sin^2\!A + \cos^2\!A) + 2\sin A\cos A} $
. . . . . . . . . . $\displaystyle =\;\dfrac{\sin^2\!A - \cos^2\!A}{\sin^2\!A + 2\sin A\cos A + \cos^2\!A} $
. . . . . . . . . . $\displaystyle =\;\dfrac{(\sin A - \cos A)(\sin A + \cos A)}{(\sin A + \cos A)^2} $
. . . . . . . . . . $\displaystyle =\;\dfrac{\sin A - \cos A}{\sin A + \cos A}$
I have to say, I generally ignore attached images of hand-written work, especially if they are oriented in any way other than that which I can easily read. So you aren't the only one who feels this way. I know from my discussions with others who help on math sites, that many feel this way too.
While I do agree that the OP is at least making an attempt to show work, which is more than many do, I just find all but the neatest of handwriting to be more effort to read than I am willing to make.