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$cos5\theta=16cos^5\theta-20cos^3\theta+5cos\theta$ This is the question I don't understand, and I don't undersatnd the markscheme either.
This question is the fifth part of a few, but here are the previous questions.
The mark scheme for e is:
I've done all the parts before this correctly, but I don't get this final part of the question. I'd really appreciate it if someone could explain all of it to me.
Let $\theta=\frac{\pi}{10}$. Then $\cos 5\theta=0$. It follows that $$16\cos^5\theta-20\cos^3\theta+5\cos\theta=0.$$ Since $\cos\theta\ne 0$, we have $$16\cos^4\theta-20\cos^2\theta+5=0.$$ This is a quadratic equation in $\cos^2\theta$. Solve, using the Quadratic Formula. There is a choice of root for $\cos^2\theta$, but it should not be difficult to select the right one.