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The ability to structure paragraphs is a quality that many students worry they do not possess. Fortunately, this is an easy and effective skill to master: once you crack the formula, your essays will appe...

There are typically 4 steps: proving the base case, making an assumption, making the inductive step and finally concluding the proof.

The base case consists of proving that a statement is true for ...

tanh(x) = ((e^x-e^-x)/2)/((e^x+e^-x)/2) 1 - tanh²(x) = 1-((e^x-e^-x)/(e^x+e^-x))²  = ((e^2x+...

2cos(2x) = 1-2sin(x)

2(1-2sin²(x)) = 1-2sin(x) -- by our trigonometric functions

2-4sin²(x) = 1-2sin(x)

4sin²(x)-2sin(x)-1=0 -- rearrange

sin(x...

There are a few different ways to approach this problem. The most obvious is to attempt to factorise x³ + 2x² - 9x - 18. However it is very difficult to approach the problem like thi...