What is the value of the following expression? $$\sin54^\circ\cos108^\circ$$
So what I tried here is:
$\sin54^\circ\cos108^\circ=\\\cos36^\circ\cos(2\cdot54^\circ)=\\\cos36^\circ(\cos^254^\circ-\sin^236^\circ)=\\\cos36^\circ\cos^254^\circ-\cos^354=\\{1\over2}\big[\cos90^\circ +\cos18^\circ \big]\cdot\cos54^\circ-\cos^336^\circ=\\{1\over2}\cos18^\circ\cos54^\circ-\cos^336^\circ$
I don't think I can do with this anything really, seems pointless to continue. Where have I gone wrong? What should've I done instead of this?
Edit: I'm a high school student, I have only done the values from the trigonometry circle. If possible, solve this without using computing of values, since I don't know how to do that at all.