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# core 2 question - sin cos tan Watch

1. Came across a question on a piece of homework but i dont quite understand how to answer it.

show that the equation tan 2x = 5 sin 2x

can be written as: (1- 5 cos 2x) sin 2x = 0

I would be comfortable answering questions similar to this however im not used to having a "2x" after a sin or cos normally just "x".

Any help would be appreciated.
Came across a question on a piece of homework but i dont quite understand how to answer it.

show that the equation tan 2x = 5 sin 2x

can be written as: (1- 5 cos 2x) sin 2x = 0

I would be comfortable answering questions similar to this however im not used to having a "2x" after a sin or cos normally just "x".

Any help would be appreciated.
Recall that

3. Since everything is in terms of 2x just leave it as is and solve as you normally would when there was an x there.

Just keep in mind that when later on, as most questions inevitably do, it asks you to solve for x. You'll need to divide all of your answers by 2.
Came across a question on a piece of homework but i dont quite understand how to answer it.

show that the equation tan 2x = 5 sin 2x

can be written as: (1- 5 cos 2x) sin 2x = 0

I would be comfortable answering questions similar to this however im not used to having a "2x" after a sin or cos normally just "x".

Any help would be appreciated.
You have an equation that includes tan2x, yet the one you want does not. You can see, however, that it has a cos2x and a sin2x. Try using an identity and then rearranging to the required form.

(Original post by Dannyboy2015)
Since everything is in terms of 2x just leave it as is and solve as you normally would when there was an x there.

Just keep in mind that when later on, as most questions inevitably do, it asks you to solve for x. You'll need to divide all of your answers by 2.
Not exactly as if it was x, because you also need to consider any additional solutions that would otherwise be outside of the range.
5. (Original post by kingaaran)
Not exactly as if it was x, because you also need to consider any additional solutions that would otherwise be outside of the range.
That is why you divide all of your answers by 2, as I mentioned. Perhaps I should have been clearer and stated that If you are solving for x in the range 0<x<360 (as an example), it follows that when you solve for 2x your range will be 0<2x<720.

At any rate, it makes no difference for the part of the question that the op asked for help with, which was rewriting:
tan 2x = 5 sin 2x as (1- 5 cos 2x) sin 2x = 0
When you have a 2x instead of an x, as opposed to solving for x.

Thanks for pointing that out.
6. (Original post by Dannyboy2015)
That is why you divide all of your answers by 2, as I mentioned. Perhaps I should have been clearer and stated that If you are solving for x in the range 0<x<360 (as an example), it follows that when you solve for 2x your range will be 0<2x<720.

At any rate, it makes no difference for the part of the question that the op asked for help with, which was rewriting:
tan 2x = 5 sin 2x as (1- 5 cos 2x) sin 2x = 0
When you have a 2x instead of an x, as opposed to solving for x.

Thanks for pointing that out.
Sorry :s I was just being annoyingly pedantic!

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