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By a certain Pythagorean identity we can say 1-cos^2(x)=?

Sin^2x?

yep! :)

We could use that same identity to rewrite cos^2(x)

\[1-\cos^2(x)=\sin^2(x) => \cos^2(x)=\]

that is a blank for you to fill in

I'm lost

\[\cos^2(x)+\sin^2(x)=1 \]

So cos^2(x)=?

Sin^x+ 1

1-sin^2(x)

Sin^2x+1?

I was close

1-cos^2(x)=sin^2(x)
1-sin^2(x)=cos^2(x)
cos^2(x)+sin^2(x)=1

I replaced mr.cos^2(x) with mrs. (1-sin^2(x))

now 1+1=2 which I know you know (:p)
so now you distribute on that left hand side

I will be here most likely. I'm not much of a facebook user. I'm on facebook free diet right now. :p