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sethmich · Mar 20, 2008, 09:28 AM

how do I verify that

(csc(x)/ 1 + csc(x)) - (csc(x)/ 1 - csc(x)) = 2 sec ^2(x)

herz · Mar 20, 2008, 11:16 AM

I could use help with this one too, I tried doing it for practice but I am struggling on what to start with, I tried a few things but nothing was working.

galactus · Mar 20, 2008, 12:46 PM

$\frac{csc(x)}{1+csc(x)}-\frac{csc(x)}{1-csc(x)}$

Cross multiply:

$\frac{csc(x)-csc^{2}(x)-csc(x)-csc^{2}(x)}{(1+csc(x))(1-csc(x))}$

$\frac{-2csc^{2}(x)}{1-csc^{2}(x)}$

Note that $1-csc^{2}(x)=-cot^{2}(x)$

$\frac{2csc^{2}(x)}{cot^{2}(x)}$

Now, can you finish? Write it in terms of sin and cos and you should be able to see it?