Question

how do I simplify sqrt(1-cos^2(2x))? I think I should get sin(2x)

Answer 1

yes that is correct

Answer 2

oh wait do I just sub in sin^2 for 1-cos^2?

Answer 3

yep...pythagorean identity

Answer 4

Say we have \(y=\sqrt{1-cos^2(2x)}\)
Squaring both sides gives:
\(y^2=1-cos^2(2x)\)
So \(y^2 + cos^2(2x)=1\)
We know that for any angle, \(sin^2+cos^2=1\). So y is clearly \(sin(2x)\).

Does that explanation make sense?

Answer 5

yes thank you

Answer 6

No worries :)