Question

prove cosx-sinx/cosx+sinx = sec2x-tan2x

Answer 1

Answer on Question #49366 – Math – Trigonometry

Prove cosx-sinx/cosx+sinx = sec2x-tan2x

Solution.

$$\frac {\cos x - \sin x}{\cos x + \sin x} = \frac {(\cos x - \sin x) ^ {2}}{(\cos x + \sin x) (\cos x - \sin x)} = \frac {\cos^ {2} x - 2 \sin x \cos x + \sin^ {2} x}{\cos^ {2} x - \sin^ {2} x} = \frac {1 - 2 \sin x \cos x}{\cos 2 x} = \frac {1 - \sin 2 x}{\cos 2 x} = \frac {1}{\cos 2 x} - \tan 2 x = \sec 2 x - \tan 2 x.$$

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