Identities Help

[Guest Skara]

Gah!! I've tried and tried. Can someone please help me real quick with these two identities?

 

[math]sin^2(x)(1 + cot^2(x)) = 1[/math]

 

and

 

[math]tan(x) + cot(x) = sec(x)csc(x)[/math]

 

I keep getting places, but nowhere helpful...

 

Edit: LaTeX. nice. ^^;

[Ducky Havok]

For the first one, just foil it out and rewrite [math]cot^{2}(x)[/math] as [math]\frac{cos^{2}(x)}{sin^{2}(x)}[/math]. You get [math]sin^{2}(x)+cos^{2}(x)=1[/math] which is a common identity.

 

For the second, rewrite it as [math]\frac{sin(x)}{cos(x)}+\frac{cos(x)}{sin(x)}[/math]. After you cross multiply and add them together, you get [math]\frac{sin^{2}(x)+cos^{2}(x)}{cos(x)sin(x)}[/math]. The top is equal to 1 (the identity in your first problem), and when you break apart the bottom and rewrite it it is [math]sec(x)csc(x)[/math]

[Guest Skara]

Thank you!! Sometimes it just takes another pair of eyes!

 

You've been a big help.

 

--Skara