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The infinite series C and S are defined C = acos(x) + a^2cos(2x) + a^3cos(3x) + ..., and S = asin(x) + a^2sin(2x) + a^3sin(3x) + ... where a is a real number and |a| < 1. By considering C+iS, show that S = asin(x)/(1 - 2acos(x) + a^2), and find C.

C + iS = (acos(x) + a^2cos(2x) + a^3cos(3x) + ...) + i( asin(x) + a^2sin(2x) + a^3sin(3x) + ...)

= a(cos(x) + isin(x)) + a^2(cos(2x) + isin(2x)) + a^3(cos(3x) + ...

Answered by Salman F. • Further Mathematics tutor

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What is the mechanism for the nucleophilic substitution of a halogenoalkane?

A halogenoalkane is a saturated hydrocarbon chain with a halogen atom (F, Cl, Br or I) attached to a carbon instead of a hydrogen. Halogens have a greater electronegativity than carbon. This means they dr...

Answered by Charlotte S. • Chemistry tutor

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How do you intergrate a function?

Increase the powers of all variables by one and then divide them by this number. For example, given 3x^3 + 5x^-0.5 - 8 , this would give 3/4x^4 + 10x^0.5 - 8x

Answered by David C. • Maths tutor

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What is a mole?

A mole is the amount of a substance which contains as many particles (atoms, ions, molecules etc) of the substance as there are carbon atoms in 12g of ¹²C - this is exactly 6.02 × 10²³

Answered by Molly N. • Chemistry tutor

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What is the difference between classical and operant conditioning? Give an example of each.

Classical conditioning is the behavioural process through which the subject will exhibit a behaviour in response to a conditioned stimulus; the conditioned stimulus having previously become associated wit...

Answered by Molly N. • Psychology tutor

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The infinite series C and S are defined C = acos(x) + a^2cos(2x) + a^3cos(3x) + ..., and S = asin(x) + a^2sin(2x) + a^3sin(3x) + ... where a is a real number and |a| < 1. By considering C+iS, show that S = asin(x)/(1 - 2acos(x) + a^2), and find C.