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Derive double angle formulas from addition formulae

sin2x = 2sinxcosxcos2x = cos 2 x - sin 2 x=2 cos 2 x - 1= 1 - 2sin 2 xtan2x = (2tanx)/(1-tan 2 x)
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Answered by Alexander H. • Maths tutor
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Find the equation of the normal to the curve x^3 + 2(x^2)y = y^3 + 15 at the point (2, 1)

The first thing when seeing such a question is to find out what the question wants you to do and plan your method to do so.In this case, the question asks you to find the normal of a curve at a given point (...
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Answered by Kelvin L. • Maths tutor
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The equation kx^2+4kx+5=0, where a is a constant, has no real roots. Find the range of possible values of k.

First, if k=0 then the equation has no real roots since in this case we would have 5=0 (this is a proof by contradiction). A quadratic equation of the form ax^2+bx+c=0 has no real roots if the discriminant b...
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Answered by Emily N. • Maths tutor
14372 Views

How do you differentiate?

Say you have the term y=3X 2 . You start by bringing the power down and placing it in front of the 3 so they multiply like so y=2x3X 2 then next you take one away from the power like so y=2x3X 1 . This can t...
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Answered by Alex Y. • Maths tutor
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p(x)=2x^3 + 7x^2 + 2x - 3. (a) Use the factor theorem to prove that x + 3 is a factor of p(x). (b) Simplify the expression (2x^3 + 7x^2 + 2x - 3)/(4x^2-1), x!= +- 0.5

(a) The factor theorem states that: the polynomial f(x) has a factor (x - a) if and only if f(a) = 0.Use that information, we know that (x + 3) is a factor of p(x) if p(-3) = 0. So let's test it:p(-3) = 2(-3...
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Answered by James M. • Maths tutor
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