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# trig equation

1. How would you solve this without a calculator:

cosx + cos3x = sinx +sin3x

Between 0 and 2pi
2. (Original post by pippabethan)
How would you solve this without a calculator:

cosx + cos3x = sinx +sin3x

Between 0 and 2pi
Apply double angle would be the obvious way. I don't have time at the moment so I can't provide you with an alternative. Try to get it in terms of a single trig function with double angle.
3. use the second from bottom and fourth from bottom of these relationships:*

4. Use the factor formulae
5. This is what I've got so far. I know that sin3x can be simplified in terms of sinx only but I can't see how that would help. Any hints?
Attached Images

6. (Original post by pippabethan)
This is what I've got so far. I know that sin3x can be simplified in terms of sinx only but I can't see how that would help. Any hints?
You're making it way too complicated - look at the formulae provided by thebear in post #3. These should also be in your formula book - ways of rewriting sin A + sin B and cos A + cos B
7. I had a go but it got a bit nasty & complicated
Attached Images

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