Question

вычислите логарифмы с синусами и косинусами

Answer 1

а)
${1over3}log_4sin^3{13piover6}=log_4 sin{13piover6}=log_4sin(2pi+{piover6})=log_4sin({piover6})=\=log_4{1over2}=-{1over2}\log_4sin{piover12}+log_4sin{7piover12}=log_4sin{piover12}sin{7piover12}=\=log_4{1over2}(cos(-{6piover12})-cos({8piover12}))=log_4{1over4}=-1\-1-{1over2}=-1.5$

б)
$cos{piover8} textgreater sin{piover8}Rightarrow{1over2}log_8(cos{piover8}-sin{piover8})^2=log_8(cos{piover8}-sin{piover8})\-log_8(cos{piover8}+sin{piover8})^{-1}=log_8(cos{piover8}+sin{piover8})\log_8(cos{piover8}-sin{piover8})+log_8(cos{piover8}+sin{piover8})=log_8(cos^2{piover8}-sin^2{piover8})=\=log_8{cos{piover4}=log_8{1oversqrt2}=-{1over6}$