If . Find the value of .

Thanks.

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- Dec 8th 2010, 04:19 AMdynamicsagarTrig Question - Help Needed
If . Find the value of .

Thanks. - Dec 9th 2010, 08:24 AMOpalg
__Stage 1.__What does the given information tell you? Multiply out the fractions and it becomes . Using standard trig formulas for sines and cosines , you can write this as .

__Stage 2.__Can you think of any examples where that condition is satisfied? One way to get is if and . That will occur for example if and . Then , and (see here) . For that example, , which simplifies (details omitted – do the calculation to check that it works) to 1.

__Stage 3.__Make a wild guess.*Could it*__always__be true that (given that )?

__Stage 4.__See if you can prove that the guess in Stage 3 is correct. If it is, then multiplying out the fractions means that we want to show that . Let's see: