SOLUTION: Cot a-1/1-Tan a = Csc a/Sec a

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Question 39170: Cot a-1/1-Tan a = Csc a/Sec a
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+%28cotA-1%29%2F%281-tanA%29+
lets just manipulate the numerator first: +%28cotA-1%29+
+%28%28cosA%29%2F%28sinA%29%29-1+
+%28%28cosA%29%2F%28sinA%29%29-%28%28sinA%29%2F%28sinA%29%29+
+%28%28cosA%29-%28sinA%29%29%2F%28sinA%29+

and now the denominator: +%281-tanA%29+
+1-%28%28sinA%29%2F%28cosA%29%29+
+%28%28cosA%29%2F%28cosA%29%29-%28%28sinA%29%2F%28cosA%29%29+
+%28%28cosA%29-%28sinA%29%29%2F%28cosA%29+

So we have:

which is

+%28cosA%29%2F%28sinA%29+

So the question now is, does +%28cosA%29%2F%28sinA%29+ equal +%28cosecA%29%2F%28secA%29+?

Well, +%28cosecA%29%2F%28secA%29+ is
+%281%2F%28sinA%29%29%2F%281%2F%28cosA%29%29+

which can be rearranged into:
+%281%2F%28sinA%29%29%28%28cosA%29%2F1%29+
+%28cosA%29%2F%28sinA%29+
so yes.


jon.