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There are two approaches to rationalising a denominator depending on how the denominator appears. First we deal with the simpler case where the surd term is the only term in the denominator. For example: 6/√...

From the addition formula, we know that: Rcos(x-c) = Rcos(x)sin(c)+Rsin(x)cos(c) Therefore: acos(x)+bsin(x) = Rcos(x)cos(c)+Rsin(x)sin(c) If we equate the coefficients of cos(x) and sin(x) we see that: acos(...

If you were to draw a graph of the function, a stationary point would be a point on the graph where the gradient is zero, i.e the graph has no vertical slope. For example consider the function f(x) = 2. This...

To differentiate this, we must use the Chain Rule . This is because we have two functions multiplied by each other: (x) sin⁡(x). We use the substitution u = sin(x). This is our initial function, and we can s...

The first thing to remember is that the tangent to the curve at a given point has the same gradient as the curve at that point. Let's consider the general case y=f(x) at a point c=(x1,y1). Step 1:We have to ...