SOLUTION: Can someone help? Should I use half angle identities to prove this or other identities? Thank you. (cos(1/2 x)+sin(1/2 x))/(cos (1/2 x)-(sin(1/2 x))=secx+tanx

Question 1107661: Can someone help? Should I use half angle identities to prove this or other identities? Thank you.
(cos(1/2 x)+sin(1/2 x))/(cos (1/2 x)-(sin(1/2 x))=secx+tanx
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
please help me to prove this. Thank you.
(cos(1/2 x)+sin(1/2 x))/(cos (1/2 x)-(sin(1/2 x))=secx+tanx
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Half-angle formulas are usually messier than double angle formuals.
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Start with this:

If that's confusing, sub y for x/2:
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cos(2y) = cos^2(y) - sin^2(y) = (cos(y)-sin(y))*(cos(y)+sin(y))
Multiply by (cos(y)-sin(y))
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QED
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