Expert: Steve Holleran - 3/11/2008

Question
cos2x/1-cos2x=cot2x, and sinxsecx+cotx=1/sinxcosx

we have to prove this identity, and i need help, please help me ASAP!!!!!!!!!

Answer
Hi Anum,

There is something incorrect with this first verification problem.
You can't prove it, because its not true.  Could you check that you entered it correctly, and possibly re-submit?  If you graph each side, the graphs don't coincide, which they would if the identity were true.

On the second one, try this:

  sin x * sec x + cot x = sin x * (1/ cos x) + (cos x / sin x)
                       
                        = (sin x / cos x) + (cos x / sin x)

Common denominator:  cos x * sin x:

= (sin x / cos x)(sin x / sin x) + (cos x / sin x)(cos x / cos x)

= (sin^2 x / cos x sin x) + (cos^2 x / cos x sin x)

= (sin^2 x + cos^2 x) / (cos x sin x)

Pythagorean identity:

=         1  / (cos x sin x)


Let me know about that other one.

Steve