Algebraically, how are −ln|cscx+cotx|+C and ln|cscx−cotx|+C equal? I know both of these are the answer to ∫cscx dx, and I am able to work them out with calculus using the formulas: int cscx dx =int csc x (csc x - cot x )/( csc x - cot x) dx and =int csc x (csc x + cot x )/( csc x + cot x) dx Still, when looking at the results, −ln|cscx+cotx|+C and ln|cscx−cotx|+C , I don't see how these are algebraically equivalent. Perhaps I'm just unaware of some algebra rule (that is likely!). I tried using the Laws of Logs and that doesn't help. Or maybe I'm missing some trig trick.

$\frac{20b}{{\left(4b^3\right)}^3}$

Which operation could we perform in order to find the number of milliseconds in a year??
${\displaystyle 60\cdot 60\cdot 24\cdot 7\cdot 365}$
${\displaystyle 1000\cdot 60\cdot 60\cdot 24\cdot 365}$
${\displaystyle 24\cdot 60\cdot 100\cdot 7\cdot 52}$
${\displaystyle 1000\cdot 60\cdot 24\cdot 7\cdot 52?}$

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A) No
B) 0
C) Yes
D) 6

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149600000000 is equal to
A)$1.496\times <!--\; \times \; -->{10}^{11}$
B)$1.496\times <!--\; \times \; -->{10}^{10}$
C)$1.496\times <!--\; \times \; -->{10}^{12}$
D)$1.496\times <!--\; \times \; -->{10}^8$

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