Why are both answers true?

That v was supposed to be an x

File: halftangentformula.png (3KB, 186x61px) Image search: [Google] [Yandex] [Bing]

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>>27216
It follows from the half angle formula, pic related, you can see it proven at http://www.intmath.com/analytic-trigonometry/4-half-angle-formulas.php

Also, keep in mind

csc(x)=1/secx,
ctg(x)=1/tan(x)=cos(x)/sin(x)

With that and the half angle formula you'll see that the two expressions inside the natural logarithm are equivalent.

File: 1374085092772.jpg (322KB, 900x798px) Image search: [Google] [Yandex] [Bing]

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>>27216
Now.
I pride myself as being a pretty clever guy, but I haven't a single fucking clue as where to even fucking begin deciphering these types of things.

>>27294
It's a matter of studying this stuff, no one is born knowing calculus. Media portrays math awfully, as something you just get or not, no matter if you have seen the bloody notation ever before in your life, because writers don't tend to be good at math, and stereotypes perpetuate.

>>27293
Thanks man.