Expert: David Hemmer - 7/15/2007

Question
QUESTION: I am having trouble proving the following identity.  Any hints or ideas would be greatly appreciated.
(1+tan x + cot x)(cos x -sin x) = (csc x/sec^2 x)-(sec x/csc^2 x)

ANSWER: Try writing everything in terms of sin and cos:

(1+sin/cos + cos/sin)(cos-sin)=((1/cos)/(1/sin^2) - ((1/cos)/(1/sin^2))

multiply it all out and see what happens!

---------- FOLLOW-UP ----------

QUESTION: okay so now I have (cos x - sin x)(sin x cos x +1)/(sin x cos x)= (cos^3 x sin ^3 x)/(sin x cos x)  and i am not sure how make the two sides equal.  I have been wracking my brain to no avail.  Also I was wondering about another problem I am having.

How does 2sin^x+(pi/4) relate to the cofunction identities?

Answer
I don't see what you did but you didn't do it correctly. You should get:

(1+ sin/cos + cos/sin)(cos - sin)= cos^2/sin - sin^2/cos

Now when you multiply the left hand side out you will get some cancellations and it will equal exactly to the right hand side.

As for the other question I have no idea what you mean by "cofunction identities" sorry. There are an awful lot of trig identities and they don't really have standard names.