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Proof : Key Stage 5 (A2-Level) : Mathematics Content Knowledge

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Key Stage 5 (A2-Level)
Question 1 of 1

1. How confident are you that you can give a clear and convincing argument to show:

a. the validity of a mathematical statement?


Example 1 Examples 2 & 3

Prove that the derivative of tan x is sec2 x.

	an x = \frac{{\sin x}}{{\cos x}}


\frac{d}{{dx}}\left( {	an x} 
ight) = \frac{d}{{dx}}\left( {\frac{{\sin x}}{{\cos x}}} 

Let u = sin x and v = cos x. Then:

\frac{{du}}{{dx}} = \cos x  and  \frac{{dv}}{{dx}} =  - \sin x

Using the quotient rule for differentiation

\frac{d}{{dx}}\left( {\frac{{\sin x}}{{\cos x}}} 
ight) = \frac{{\cos x\cos x + \sin x\sin x}}{{\cos ^2 x}}

 = \frac{{\cos ^2 x + \sin ^2 x}}{{\cos ^2 x}} = \frac{1}{{\cos ^2 x}}

 = \sec ^2 x

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