Question

Rewrite with only sin x and cos x.

sin 2x - cos x
Options are:

2 sin x cos^2x

sin x

cos x (2 sin x - 1)

2 sin x

Answer 1

Tell me what you get when you expand
\[\sin(2x)\]
Use your double angle results.
\[\sin(2x)=\sin(x+x)\]
\[\sin(x+x)=?\]

Answer 2

Doesn't sin 2x = 2 sin x cos x?

Answer 3

Does that have anything to do with this problem?

Answer 4

Yes.

Answer 5

That's exactly right.

Answer 6

You substitute 2sinxcosx with sin(2x).

Answer 7

so factorise 2sinxcosx-cosx for me please.

Answer 8

Well since there is cos x on both side of the equation would you cancel them and then you are left with just 2 sin x?

Answer 9

Do you know what factorising is?

Answer 10

For example, can you factorise:
\[x^2+x\]?

Answer 11

would it be x(x+1)

Answer 12

Correct! That's how you would go about factorising this:
2sinxcosx-cosx

Answer 13

Take the common factor in both terms and then you can factorise it.

Answer 14

Would the common factor would be cos x?

Answer 15

Yes!

Answer 16

So the answer would be cos x(2 sin x-1)?

Answer 17

Correct. Well Done.

Answer 18

Thank you for your help! :)

Answer 19

No worries.

Answer 20

useful to know


sin or cos shifted a certain amount will equal cos or sin.

so in other words an example

sin(x+a)=cos (x)