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We can understand this identity in two different, useful ways. Firstly, we can use Euler's identities from trigonometry to obtain the desired result using straightforward algebra. We know that: [1] sin(x) = ...

Consider the triangle ABC. Denote h the altitude through B and D the point where h intersects the (extended) base AC Cosine function for triangle ADB. cos α= x/c => x=c*cos α Pythagorean theorem for trian...

Using: Tan(x) = Sin(x)/Cos(x) Using: Cos(x) = sqrt(1-Sin 2 (x)) Cos(A) = sqrt(1-Sin 2 (A)) = sqrt(1-1/3) = sqrt(2)/sqrt(3) Therefore: Tan(A) = Sin(A)/Cos(A) = (1/sqrt(3))/(sqrt(2)/sqrt(3)) = 1/sqrt(2)

The "chain rule" is a handy little tool that we can use to find the derivative of a complicated function. Specifically, we use the chain rule when we have functions within functions. But what does ...

Quick maths.