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In these sorts of problem what you have to do is play around for ages until you can find a way of making use of things such as:
and
Until you can make some terms disappear or prove what you're asked to prove. Here we have no idea what the final answer is going to be so the first place is to look to see what you can do.
Now we now that:
and
So looking firstly at the bottom of our fraction, we see that it has a sec-squared + csc-squared term, which is:
To add these two fractions, make sure they have the same denominator ("thing on the bottom") - so multiply the first one by 1 = cos^2/cos^2, and the second by 1 = sin^2/sin^2, to give:
Now, at last, we can use on the top of this new fraction to get:
or just:
So, remarkably, the addition has just turned into multiplication! Anyway, we can now put this back into the original expression:
And cancel the common factors of and on top and bottom to get:
Where the final step comes rom the definition of . Hope this is clear and helps.

26 November 2012

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