<s>[INST] Simplify trig identity So I am having a hard time with this math question:
$$1-2\sin ^2(x)+\sin^4(x)$$
The prompt is to factor the trigonometric equation and simplify. I get it simplified to a point but the answer I keep getting is:
$$(1 + \sin^2(x))(\cos^2(x))$$
For some reason the answer key says the answer is $\cos^4(x)$ but I have no idea how they are getting to that conclusion.
 [/INST] Method-1: 
$$1-2\sin^2 x+\sin^4 x=(1)^2-2(1)(\sin^2 x)+(\sin^2 x)^2$$
By applying $a^2-2ab+b^2=(a-b)^2$
$$=(1-\sin^2 x)^2$$
$$=(\cos^2 x)^2$$
$$=\color{red}{\cos^4 x}$$
Method-2: 
$$1-2\sin^2 x+\sin^4 x=1-\sin^2 x-\sin^2 x+\sin^4 x$$
$$=(1-\sin^2 x)-\sin^2 x(1-\sin^2 x)$$
$$=\cos^2 x-\sin^2 x(\cos^2 x)$$
$$=\cos^2 x(1-\sin^2 x)$$
$$=\cos^2 x(\cos^2 x)$$
$$=\color{red}{\cos^4 x}$$
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