Evaluate
\sin(6\alpha )+\cos(5\alpha )-\cos(7\alpha )
Differentiate w.r.t. α
144\left(\cos(\alpha )\right)^{2}\left(\sin(\alpha )\right)^{5}-260\left(\sin(\alpha )\right)^{3}\left(\cos(\alpha )\right)^{4}+40\sin(\alpha )\left(\cos(\alpha )\right)^{6}-4\left(\sin(\alpha )\right)^{7}+90\left(\cos(\alpha )\right)^{2}\left(\sin(\alpha )\right)^{4}-90\left(\sin(\alpha )\right)^{2}\left(\cos(\alpha )\right)^{4}+6\left(\cos(\alpha )\right)^{6}-6\left(\sin(\alpha )\right)^{6}+53\left(\cos(\alpha )\right)^{2}\left(\sin(\alpha )\right)^{3}-22\sin(\alpha )\left(\cos(\alpha )\right)^{4}-5\left(\sin(\alpha )\right)^{5}+6\sin(\alpha )\left(\cos(\alpha )\right)^{2}-3\left(\sin(\alpha )\right)^{3}
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