alice77222 said:
I'm stuck on the last two questions of my math assignment. I'm supposed to prove identities by working the left side until it matches the right.
m) 1/(secx + 1) = cot^(2)x secx - cot^(2)x
n) (cotx)/(cscx-1)= cscx tanx + tanx
I've been working on these two questions for almost a half hour now and haven't made any progress. Help, please?
We'd assume that "working for almost a half hour" would produce SOME results....even if you didn't get the problem correct. And, if we can see what you've tried, we can also see where you might be going wrong. It is ALWAYS best to show your work, even if you think it is incorrect.
That said, I'll help you with the first one. We will, as directed, work with the left side. Multiply numerator and denominator by (sec x - 1):
1*(sec x - 1)
----------------
(sec x + 1)(sec x - 1)
1*(sec x - 1)
---------------
sec^2 x - 1
Ok....look at the fundamental identities. You should find one that says
tan^2 x + 1 = sec^2 x
If we subtract 1 from both sides of this, we get
tan^2 x = sec^2 x - 1
That means we can substitute tan^2 x for the denominator of the fraction:
1*(sec x - 1)
--------------
xxxtan^2 x
or,
xx1
----- * (sec x - 1)
tan^2 x
And what is 1/tan^2 x? Isn't that cot^2 x? So, we have
cot^2 x ( sec x - 1)
Now, just distribute the multiplication, and you're done.
You can use a similar approach on the second problem.
