<PRE><B>Question 549269</B>
prove that :

1. 1+sin A/cos A = sec A + tan A
Change to sines and cosines:
1+sin A/cos A = sec A + tan A
(1 + sin)/cos = 1/cos + sin/cos = (1 + sin)/cos QED
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2. 1-(cos^2 A/1+sinA)= sin A
Multiply thru by (1 + sin)
1+sin - cos^2 = sin + sin^2
Add cos^2
1 + sin = sin + sin^2+ cos^2
sin^2 + cos^2 = 1 (Pythagorean Identity)
= sin + 1  QED
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3. cscA-cotA = sinA/1+cosA
change to sines and cosines.  email via the TY note for help if needed.
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4. sec A - tan A = cos A/1+sinA
change to sines and cosines.  email via the TY note for help if needed.
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5. (1+tanA)/(1-tanA) = (cotA+1/cotA-1)
change to sines and cosines.  email via the TY note for help if needed.
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To do these, you just try things.  
Change to sines and cosines and look for something you recognize.
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