Expert: Socrates - 7/22/2009

Question
1+sec A/sec A = sin^2/1-cos A   establish an identity...i
got all the work, but some where im doing something wrong
Here is my work:

1+1/cos A / 1/cos A

cos A +1/cos A/1/cos A

then i bring up the bottom to the top and i end up with
cos A +1 ? please help, thank you !!

Answer
Your work is correct as far as it goes.

The left side is cos A + 1 , as you have found .

But the right side is  sin^2/1-cos A = (1 - cos^2 A )/ (1 - cos A )

Factor the numerator (1 - cos^2 A ) =  (1 - cos A )(1 + cos A )

so  sin^2/1-cos A = (1 - cos A )(1 + cos A )/ (1 - cos A ) = 1 + cos A

Which is the same as the left side.


If you prefer , you can just keep working with the left side

cos A + 1 = (1 + cos A )/ 1  = (1 - cos A )(1 + cos A )/ (1 - cos A ) =

(1 - cos^2 A )/ (1 - cos A ) = sin^2/(1-cos A)