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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 should I write my answer to "Why do you want to study medicine?"

There is no need to rehearse a whole answer, and typically interviewers are not a fan of this anyway, since it is often obvious when an answer sounds recited. So just collect your thoughts on your main po...

Answered by Molly A. • Medical School Preparation tutor

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How do you write a personal statement?

You avoid the cliches and seek out what the university you desire to study at values. You can do this by assessing their aims as private businesses and educational institutions, see what you have in your ...

Answered by • Personal Statements tutor

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