Need help with identities.

[Guest]

Ok, so i need some help please with this.

Rationalize the denominator

(I'm not sure how to enter square root, so i'll just use sqrt)

sqrt(cos^2y/2sin^2y)

thanks for the help in advance

 

[tkhunny]

There's quite a bit going on in this one. I'm not sure how much of it you want.

\(\displaystyle \L\,\sqrt{\frac{cos^{2}{y}}{2*sin^{2}{y}}}\,=\,\frac{1}{\sqrt{2}}*\frac{\sqrt{cos^{2}{y}}}{\sqrt{sin^{2}{y}}}\,=\,\frac{1}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}*\frac{|cos(y)|}{|sin(y)|}\,=\,\frac{\sqrt{2}}{2}*\frac{|cos(y)|}{|sin(y)|}\)