Вычислите значение выражения log32(sin5П/8)+log32(sin6П/8)+log32(sin7П/8)
а второе выражение без синусов да?
с синусом
==-0.4 sin6π/8=sin3π/4=sin(π-π/4)=sinπ/4=√2/2 sin5π/8×sin7π/8=1/2(cos2π/8+cos12π/8)=1/2(cosπ/4+cos3π/2)=1/2(√2/2+0)=√2/4 ответ: -0,4
![log_{32} (sin5pi/8*sin6pi/8*sin7pi/8)=[tex]log_{32} ( \frac{ \sqrt{2} }{2}* \frac{ \sqrt{2} }{4} )= log_{32}(1/4)=-2/5](https://tex.z-dn.net/?f=+log_%7B32%7D+%28sin5pi%2F8%2Asin6pi%2F8%2Asin7pi%2F8%29%3D%5Btex%5Dlog_%7B32%7D+%28+%5Cfrac%7B+%5Csqrt%7B2%7D+%7D%7B2%7D%2A+%5Cfrac%7B+%5Csqrt%7B2%7D+%7D%7B4%7D++%29%3D+log_%7B32%7D%281%2F4%29%3D-2%2F5 "log_{32} (sin5pi/8*sin6pi/8*sin7pi/8)=[tex]log_{32} ( \frac{ \sqrt{2} }{2}* \frac{ \sqrt{2} }{4} )= log_{32}(1/4)=-2/5")
=-0.4