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Using z=cos(θ)+isin(θ), find expressions for z^n-1/z^n and z^n+1/z^n

We make use of De Moivre's Theorem which states that (cos(θ)+isin(θ))^n=cos(nθ)+isin(nθ).z^n-1/z^n=cos(nθ)+ isin(nθ)-cos(-nθ)- isin(-nθ)=cos(nθ)+ isin(nθ)-cos(nθ)+ isin(nθ) (by trig relat...

Answered by Bogosi S. • Further Mathematics tutor

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Explain 2 Advantages of Using Die Casting over Sand casting for the manufacturing of a Metal Engine Block.

Options: (1 mark for 1 Advantage, 1 mark for 1 Explanation)Die casting has a better surface finish (1 mark). This Allows for a reduction of additional processes needed to finish the product which can make...

Answered by Ben S. • Design & Technology tutor

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Prove that 2Sec(x)Cot(x) is identical to 2Cosec(x)

2 Secx = 2/CosxCotx = 1/Tan x = Cosx/SinxTherefore: 2SecCotx = 2/Cosx * Cosx/Sinx = 2/Sinx = 2Cosecx

Answered by Ben S. • Maths tutor

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How do I approach: "Explore the significance of justice and injustice in two crime texts you have studied"

This type of question crops up in the AQA A Level English Lit B in papers 1 and 2 for both options (here it is for Crime, but also applicable for Tragedy, Comedy and Social/Political Protest). The questio...

Answered by Sam S. • English Literature tutor

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How do I write a comparative essay?

The key to a comparative essay is to be consistent with your comparisons throughout. As with all essays, your theme and argument should be present from your introduction and run through to your conclusion...

Answered by • English tutor

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