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Prove that cos(4x) = 8(cos^4(x))-8(cos^2(x)) + 1

cos(4x) = cos(2(2x)) = 2(cos^2(2x)) - 1 = 2 (cos^2(x) - 1)^2 - 1 = 8(cos^4(x)) - 8(cos^2(x)) + 1
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Answered by Harry T. • Maths tutor
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Explain the bonding and thus the properties of a carbon allotrope

Diamond- Each carbon atom is bonded to four other carbon atoms with strong covalent bonds in a tetrahedral structure (with bond angles of 104.9 degrees). As all four valence electrons are used for bonding, n...
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Describe the process of DNA replication

In DNA replication, first the hydrogen bonds between the nitrogenous bases are broken catalysed by the enzyme helicase, causing the DNA double helix to unwind and unzip, leaving the nitrogenous bases exposed...
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Answered by Helena N. • Biology tutor
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How would you integrate (4x+1)^1/3 ?

Firstly, increase the power outside the brackets by 1 and divide the whole thing by the new power. This gives 3/4(4x+1) 4/3 Next, divide the whole thing by the derivative of the bracket. The derivative of (4...
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Answered by Nicholas G. • Maths tutor
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Describe the process of phagocytosis and how antigen presentation leads to antibody production (9 marks)

White cell (macrophage/neutrophil) detects bacteria antigen by binding to cell surface receptorsWhite cell engulfs bacteria (this is endocytosis), bacteria is held in a phagosome Lysosomes enter phagosome an...
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Answered by Caine R. • Biology tutor
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