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# C3 Trigonometry Question

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1. Hello all,
I would be most grateful if anybody could help me with the following trigonometry question:

Write the following as a single trig ratio:
a) 1/2 cos x - (root 3)/2 sin x

The correct answer in specified as cos(x+60) or sin(30-x), however I am having difficulty trying to get those answers.

Any help would be greatly appreciated!

Regards,
Aaron.
2. Substitute: 1/2 = cos60 and (root 3)/2 = sin60.

Then use the formula: cos(A+B) = cosAcosB - sinAsinB.

This will get you cos(60 + x).
3. The general way to do these problems is to write .
In this case you can see that and .
You can solve for both and .
4. Thank you very much!

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