(Maths help) How do I simplify. this expression?

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Heli2022
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Its from STEP 2019 P2 Q4 for reference
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mqb2766
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(Original post by Heli2022)
Its from STEP 2019 P2 Q4 for reference
Are you asking how they took one term out the product and multiplied by sin?
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Heli2022
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(Original post by mqb2766)
Are you asking how they took one term out the product and multiplied by sin?
No I mean like how do I go about simplifying the last term on the board to something where it is only in terms of either sinx or cosx
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DFranklin
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(Original post by mqb2766)
Are you asking how they took one term out the product and multiplied by sin?
I think that's their starting attempt to simplify it.
My own first instinct was to rearrange 2 sin x cos x = sin 2x to get an expression for 2 cos x in terms of sin 2x and sin x. At this point it is fairly obvious how the sum simplifies, although if it's not, explicitly writing out a few terms should seal the deal.
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Heli2022
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(Original post by DFranklin)
I think that's their starting attempt to simplify it.
My own first instinct was to rearrange 2 sin x cos x = sin 2x to get an expression for 2 cos x in terms of sin 2x and sin x. At this point it is fairly obvious how the sum simplifies, although if it's not, explicitly writing out a few terms should seal the deal.
I am having difficulties simplifying the sum to be honest could you help explain how it would be done?
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DFranklin
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You should have an identity expressing cos x in terms of sin 2x and sin x.

Use the same identity to express cos(x/2) in terms of sin x and sin(x/2).

This lets you find cos x cos(x/2).

Now, what happens if you use the same identity to multiply by cos(x/4)?

And so on...
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