Question

!!?!! дам 25 баллов!!!!

Answer 1

$4);frac{tg7alpha-tg3alpha}{tg7alphacdot tg3alpha+1}=tg(7alpha-3alpha)=tg4alpha\\5);cos^2alpha-4sin^2fracalpha2cos^2fracalpha2=cos^2alpha-(2sinfracalpha2cosfracalpha2)^2=cos^2alpha-(sinalpha)^2=\=cos^2alpha-sin^2alpha=cos2alpha$

$6);sqrt{1+cos8alpha}=sqrt{1+2cos^24alpha-1}=sqrt{2cos^24alpha}=sqrt2cdotcos4alpha\\7);frac{sinalphacosalpha}{1-2sin^2alpha}=frac{frac12sin2alpha}{cos2alpha}=frac12tg2alpha$