Question

Factor and simplify
Sin4x-cos4x

Answer 1

$$\sin 4x - \cos 4x = \sin 4x - \sin \left(\frac {\pi}{2} - 4x\right) = 2 \sin \left(4x - \frac {\pi}{4}\right) \cos \left(\frac {\pi}{4}\right) = 2 \sin \left(4x - \frac {\pi}{4}\right) \frac {\sqrt {2}}{2} = \sqrt {2} \sin \left(4x - \frac {\pi}{4}\right)$$

Answer: $\sin 4x - \cos 4x = \sqrt{2} \sin \left(4x - \frac{\pi}{4}\right)$;