Monday, 12 May 2014

trigonometry - Simplifying $sin(4x)cos(4x)$




Simplify $\sin(4x)\cos(4x)$ using double angle or compound trigonometry.





Can someone please show me how its done, Ive tried several times but no where near the answer.


Answer



The double angle formula is $ \ 2 \sin\theta\cos\theta = \sin(2\theta) \iff \sin\theta\cos\theta = \frac{1}{2} \sin(2\theta)$.



By applying this formula with $\theta = 2x$, we obtain



$$\sin4x\cos4x=\frac{1}{2} \sin(8x).$$


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