Prove that 1-tan^2x/1-cot^2x=cos^2x-1/cos^2x

Question

I need to prove this but I don't even know how to start the problem. 

Answer 1

prove (1-tan^2)/(1-cot^2)=(cos^2-1)/(cos^2)

working with the left side first...

(1-[sin^2/cos^2])

---------------------

(1-[cos^2/sin^2])

 

(cos^2-sin^2)/cos^2

------------------------

(sin^2-cos^2)/sin^2

 

(sin^2-cos^2)/(-cos^2)

---------------------------

(sin^2-cos^2)/(sin^2)

 

using the rule for division you get...

(sin^2)/(-cos^2)

 

-tan^2 for the left side

 

now work with the right side...

(cos^2-1)/(cos^2)

sin^2+cos^2=1 so cos^2-1=-sin^2

 

(-sin^2)/cos^2

 

-tan^2 for the right side also, therefore the identity has been proven