Factor the expression and use the fundamental identities to simplify $7 \sin^2 x \csc^2 x − 7 \sin^2 x$ Factor the expression and use the fundamental identities to simplify. There is more than one correct form of the answer. $$7 \sin^2 x \csc^2 x − 7 \sin^2 x$$
I'm reviewing for a test and going over my old homework, is 7 a possible solution (I'm asking because the last time I did this on my homework I got $7\cos(x)$? 
$7 \sin^2 x (csc^2 x − 1)$
$=7 \sin^2 x (1 + \cot^2x)$
$=7 \sin^2 x (1 + \frac {\cos^2x}{\sin^2x})$
$=7 \sin^2 x (\frac{\sin^2x}{\sin^2x} + \frac {\cos^2x}{\sin^2x})$
$=7\sin^2x (\frac{\sin^2x+\cos^2x}{\sin^2x})$
$=7\sin^2x (\frac{1}{\sin^2x})$
$=\frac{7\sin^2x}{\sin^2x}$
$=7$

$$7\sin^2 x\csc^2 x-7\sin^2 x=7\sin^2 x\frac{1}{\sin^2x}-7\sin^2 x=$$
$$=7-7\sin^2 x=7(1-\sin^2 x)=7\cos^2x$$
