Question 1205416
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I am using the fundamental identities to try to verify the following equation. 
It is a true statement but I find myself a little lost, probably on something basic algebra.
I primarily work on the left side and haven't really worked on the right side.
I know an identity could be verified by using many different methods, which is why the book 
I am using doesn't explain the process in the answers. So, your manner of verification 
may differ than what I am doing. Nevertheless, I'd appreciate any help.
In any case, here is the statement to be verified.
1 + sin theta/cot^2 theta = sin theta/csc theta - 1
Thank you very much for your help.
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<pre>
The identity in your post is (I copy it)

    1 + sin(theta)/cot^2(theta) = sin(theta)/csc(theta) - 1.


I read it this way - exactly as it is written in your post

    1 + {{{sin(theta)/cot^2(theta)}}} = {{{sin(theta)/csc(theta)}}} - 1.



        This identity is INCORRECT, and I will show it right now.



Take {{{theta}}} = 45°.

Then in the left side,  cot(theta) = cot(45°) = 1;  so,  cot^2(theta) = 1, and the left side is

    1 + sin(45°) = 1 + {{{sqrt(2)/2}}}.


The right side is  {{{sin(45^o)/((1/sin(45^0)))}}} - 1 = {{{sin^2(45^o)}}} - 1 = {{{(sqrt(2)/2)^2}}} - 1 = {{{2/4}}} - 1 = {{{1/2}}} - 1 = {{{-1/2}}}.


The left side 1 + {{{sqrt(2)/2}}} is not equal to the right side {{{-1/2}}},  so the identity is not hold.
</pre>

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Double check your writing in your post.