identities: 1/tanx = cotx/ sin^2x + cos^2x

[ca.chick]

i am not sure how to figure this out:

it has to be equal to each other and i got stuck:

1/tanx = cotx/ sin^2x + cos^2x

i know that I should reduce the harder side, but i dont know how it would end up to be 1/tanx

 

[galactus]

This is just a matter of observation. You're making it too difficult.

\(\displaystyle \L\\\frac{1}{tan(x)}=\frac{cot(x)}{\underbrace{sin^{2}(x)+cos^{2}(x)}_{\text{this is 1}}}\)

I hope you know that 1/tan(x)=cot(x).

See it?. You're done.