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Consider, (cosX+isinX)6 using binomial expansion we find that this = "cos6X + 6icos5XsinX - 15cos4Xsin2X - 20icos3Xsin3X +...
Proofs come in many shapes and sizes but this one is done via induction. When doing proof by induction, examiners love a list of a clear definite list of steps, the first being the base case, in t...
We know that r= 6 and θ = 3π/4 as it is given in the question. We can then use the identities: x= rcosθ and y= rsinθ to find the x and y coordinates which are the Cartesian coordinates. So, x= rcosθ = 6co...
i) multiply out: 3x3+kx2-3x-21x2-7kx+21 simplify: 3x3+(k-21)x2+(-7k-3)x+21 the coefficient of x2 is 0 and therefore k-21=0 k=21.ii)from i) the c...
For this question I would heavily emphasise layout as these questions are very strict. Base n=1 simply plug n=1 into the equation and you will find you end up with 65 which is di...
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