Need help proving trig identities?

Question

I'm having trouble proving these trig identities. Help is greatly appreciated. Thanks in advance!

 

1) 1- sinx/cosx = cosx/ 1+sinx

2) sin^2x = 1- cos^2x

3) sin2x/2sinx = cosx

4) cosx(1+ tan^2x) = secx

5) cos^4x - sin^4x = cos^2x

6) cotθ -1/ cotθ +1 = 1-tanθ/ 1+ tanθ

 

 

Thank you in advance!

Answer 1

Brianna,

1) 1- sinx/cosx = cosx/ 1+sinx

multiply through by cosx and 1+sinx and you should get

 

(1- sinx)(1+sinx) = cos²x,    (1- sinx)(1+sinx) gives you difference of two squares 1 - sin²x

 

1 - sin²x = cos²x   this is one of the trig identities you get by manipulating another trig identity sin²x+cos²x=1. just do some subtraction and you will get it. I hope this helps.