please help me with this question:

given without using calculator,find the values of .

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- Jul 5th 2010, 06:15 AMmastermin346problem in addition formulae and double angle formulae
please help me with this question:

given without using calculator,find the values of . - Jul 5th 2010, 06:43 AMeumyang
Uh... come again? Maybe I'm not seeing it, but is there more to this problem? It this part of a bigger problem?

EDIT: Do you mean this:

Quote:

given without using calculator,find the values of .

- Jul 5th 2010, 06:48 AMmastermin346
yes..that is the question.

opp..sory..the question is tan 2\theta..i have edit it - Jul 5th 2010, 07:17 AMeumyang
I'm getting

**2**answers:

I started by using the tangent double identity:

Cross-multiplied:

... solved for , then rewrote in terms of .

EDIT: I originally thought that both answers I wrote above were plus-minus, but I forgot that is positive, which means that the angle has to be in Quadrants I or III. So is between 0 and 45° or between 90° and 135°, and for those values of , sine is positive. - Jul 5th 2010, 07:20 AMProve It
You should know that

.

So if then

or

or .

Case 1:

.

This means you are dealing with a right-angle triangle of side lengths and .

By Pythagoras, that means that .

Since that means

.

Apply a similar process for Case 2.