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C3 double angle simplifying

Hi, how do you write these in their simplest forms? Hmmm

I need help with question 3 part (e), (f), (g), (h) and (i).

ImageUploadedByStudent Room1477145523.701794.jpg




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Reply 1
For part e we want to get rid of that +1 that's making this difficult. Recall that cos2θ2cos2θ1 \cos 2\theta \equiv 2\cos^2 \theta -1 . This gets rid of the +1 and you can just take square root.
WARNING: Be very careful when taking the square root.
Original post by B_9710
For part e we want to get rid of that +1 that's making this difficult. Recall that cos2θ2cos2θ1 \cos 2\theta \equiv 2\cos^2 \theta -1 . This gets rid of the +1 and you can just take square root.
WARNING: Be very careful when taking the square root.



Ah thank you! How do you do part (f)?
Reply 3
Original post by jessyjellytot14
Ah thank you! How do you do part (f)?


Simply rewrite it as (sinθcosθ)2 (\sin \theta \cos \theta )^2 and you know that sin2θ2sinθcosθ \sin 2\theta \equiv 2\sin \theta \cos \theta
ImageUploadedByStudent Room1477160082.047681.jpg

Thanks, and this is a different question but would you be able to explain why there are no cos(x)'s in the third step?

(I used x instead of theta because my keyboard doesn't have a theta symbol :frown: )

@B_9710


Posted from TSR Mobile
(edited 7 years ago)
Reply 5
Original post by jessyjellytot14
ImageUploadedByStudent Room1477160082.047681.jpg

Thanks, and this is a different question but would you be able to explain why there are no cos(x)'s in the third step?

(I used x instead of theta because my keyboard doesn't have a theta symbol :frown: )

@B_9710


Posted from TSR Mobile


As sin(AB)=sinAcosBcosAsinB \sin(A-B) = \sin A \cos B - \cos A \sin B , sin(3θθ)=sin3θcosθcos3θsinθ \sin(3 \theta - \theta) = \sin 3 \theta \cos \theta - \cos 3 \theta \sin \theta .
Reply 6
Original post by jessyjellytot14
ImageUploadedByStudent Room1477160082.047681.jpg

Thanks, and this is a different question but would you be able to explain why there are no cos(x)'s in the third step?

(I used x instead of theta because my keyboard doesn't have a theta symbol :frown: )

@B_9710


Posted from TSR Mobile


They've used double angle formula on denominator and addition formula for sine on numerator as mentioned above.
Original post by Tau
As sin(AB)=sinAcosBcosAsinB \sin(A-B) = \sin A \cos B - \cos A \sin B , sin(3θθ)=sin3θcosθcos3θsinθ \sin(3 \theta - \theta) = \sin 3 \theta \cos \theta - \cos 3 \theta \sin \theta .


Original post by B_9710
They've used double angle formula on denominator and addition formula for sine on numerator as mentioned above.


Ooooooh thanks!! I completely forgot about that :facepalm:.

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