Guest Skara Posted May 4, 2005 Share Posted May 4, 2005 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. ^^; Link to comment Share on other sites More sharing options...
Ducky Havok Posted May 4, 2005 Share Posted May 4, 2005 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] Link to comment Share on other sites More sharing options...
Guest Skara Posted May 4, 2005 Share Posted May 4, 2005 Thank you!! Sometimes it just takes another pair of eyes! You've been a big help. --Skara Link to comment Share on other sites More sharing options...
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