Question

!!?!! дам 25 баллов!!!!

Answer 1

$4)\;\frac{tg7\alpha-tg3\alpha}{tg7\alpha\cdot tg3\alpha+1}=tg(7\alpha-3\alpha)=tg4\alpha\\\\5)\;\cos^2\alpha-4\sin^2\frac\alpha2\cos^2\frac\alpha2=\cos^2\alpha-(2\sin\frac\alpha2\cos\frac\alpha2)^2=\cos^2\alpha-(\sin\alpha)^2=\\=\cos^2\alpha-\sin^2\alpha=\cos2\alpha$

$6)\;\sqrt{1+\cos8\alpha}=\sqrt{1+2\cos^24\alpha-1}=\sqrt{2\cos^24\alpha}=\sqrt2\cdot\cos4\alpha\\\\7)\;\frac{\sin\alpha\cos\alpha}{1-2\sin^2\alpha}=\frac{\frac12\sin2\alpha}{\cos2\alpha}=\frac12tg2\alpha$