[amani-puresapphire]

Can someone please explain something to me.

I know the addition formula required for this question but I dont understand how they got to the answer. Sorry im not sure how to draw the theta sign on here so I've just written the word.

The question is:

Express the following as a single sine, cosine or tangent: Cos2theta costheta + sine2theta sinetheta.

The answer is cos theta but Im not sure why. I assumed it was cos theta + sin theta.

Does anyone know how to get rid of the sin theta?

Thank you

[Hasufel]

think of this as just the expansion for "Cos(2theta-theta)" - try expanding THAT and see if you get the same

[Annalouxxxx]

I got 2costheta if that helps at all? x

[Liquidise.]

I got costheta, but I'm new to these forums and I don't know how to use proper symbols (as in formulae and such). I tried to type it but it was unreadable

[amani-puresapphire]

(Original post by Hasufel)
think of this as just the expansion for "Cos(2theta-theta)" - try expanding THAT and see if you get the same

Thank you for replying. I think im missing something here. I understand that Cos(2theta - theta) is equal to Cos theta. Im just confused why this isnt the same if you expand sine2theta sinetheta into sine (2theta - theta) to give sinetheta? I cant see it cancelled out :s

[Annalouxxxx]

Actually I got cos(theta)

cos2(theta)cost(theta) + sin2(theta)sin(theta)

cos2theta = 2cos^2-1 and sin2theta = 2sinthetacostheta

I am going to call theta x for ease

so it = (2cosx^2-1)cosx + 2sinxcosxsinx
= 2cos^3 - cos x + 2sinx^2cos x
= 2 cosx^ 3 - cos x + 2(1-cosx^2)(cos x)
= 2cos x ^3 - cos x + 2cos x - 2 cos x^ 3
= cos x

[amani-puresapphire]

Ahh thanks for trying! Is it possible to just type it anyway please? I would rather take time making sense of it than still not being able to figure it out. However if its long winded and time consuming for you, thanks again

[Liquidise.]

Haha you're more than welcome, as I didn't help at all! Did it exactly as the user above you, glad someone typed it out clearly

[Annalouxxxx]

(Original post by Liquidise.)
Haha you're more than welcome, as I didn't help at all! Did it exactly as the user above you, glad someone typed it out clearly

Is it actually understandable? I wasn't sure :P

[Liquidise.]

(Original post by Annalouxxxx)
Is it actually understandable? I wasn't sure :P

Haha yeah, it's great, nicely done couldn't figure it out myself how to write it legibly.

[amani-puresapphire]

(Original post by Annalouxxxx)
Actually I got cos(theta)

cos2(theta)cost(theta) + sin2(theta)sin(theta)

cos2theta = 2cos^2-1 and sin2theta = 2sinthetacostheta

I am going to call theta x for ease

so it = (2cosx^2-1)cosx + 2sinxcosxsinx
= 2cos^3 - cos x + 2sinx^2cos x
= 2 cosx^ 3 - cos x + 2(1-cosx^2)(cos x)
= 2cos x ^3 - cos x + 2cos x - 2 cos x^ 3
= cos x

Thanks for all the help! It sort of makes sense, i'll break it down and read it thoroughly I just noticed that the next exercise from the textbook deals with 2sintheta being equal to 2sinthetacostheta and other double angle formulae so I wasn’t aware of that particular equation. Rather unfair of them to do that!

[Annalouxxxx]

(Original post by amani-puresapphire)
Thanks for all the help! It sort of makes sense, i'll break it down and read it thoroughly I just noticed that the next exercise from the textbook deals with 2sintheta being equal to 2sinthetacostheta and other double angle formulae so I wasn’t aware of that particular equation. Rather unfair of them to do that!

That is mean! If you're stuck on any part just message me x

[amani-puresapphire]

(Original post by Annalouxxxx)
That is mean! If you're stuck on any part just message me x

Ahh I got it! I am so grateful. Between the equations for the exercise I was working on and the next, I put it all together. Trig will be the end of me I will take you up on that offer without being a pest hopefully. Self teaching myself A2 maths is troublesome. I do love the student room though

[Annalouxxxx]

(Original post by amani-puresapphire)
Ahh I got it! I am so grateful. Between the equations for the exercise I was working on and the next, I put it all together. Trig will be the end of me I will take you up on that offer without being a pest hopefully. Self teaching myself A2 maths is troublesome. I do love the student room though

Well I'm resisting this summer so its kinda helpful to be asked to work stuff out