# [25sin^2(x)+9cos^2(x)]=[9+16sin^2(x)] Why?

The Sand Man
I'm doing a problem where I need to find the maximum curvature. I'm at a point where I need to simplify the denominator and reduce the funcitions in the bottom. I don't understand how to simplify:

[25sin^2(x)+9cos^2(x)]

To:

[9+16sin^2(x)]

What is getting factored out? Or is this completing the square somehow?

Thanks for any help.

abluphoton
the simplyfication is based on the fact [ sin^2(x) + cos^2(x) = 1 ]

write down ur equation as: [ (16+9)sin^2(x) + 9cos^2(x) ] ====
[ 16sin^2(x) + 9sin^2(x) + 9cos^2(x) ] =====

[ 16sin^2(x) + 9{ sin^2(x) + cos^2(x) } ] ====

[ 16sin^2(x) + 9(1) ] ====

[ 16 sin^2(x) + 9 ]

The Sand Man
the simplyfication is based on the fact [ sin^2(x) + cos^2(x) = 1 ]

write down ur equation as: [ (16+9)sin^2(x) + 9cos^2(x) ] ====
[ 16sin^2(x) + 9sin^2(x) + 9cos^2(x) ] =====

[ 16sin^2(x) + 9{ sin^2(x) + cos^2(x) } ] ====

[ 16sin^2(x) + 9(1) ] ====

[ 16 sin^2(x) + 9 ]

Yeah I'm retarded. I knew it would be something that simple. Thanks