Question

Обчислити значення виразу log3cos2 pi/9*log cos pi/9*9

Answer 1

$\displaystyle\bf\\\log_{3} Cos^{2} \frac{\pi }{9} \cdot \log_{Cos\frac{\pi }{9} }9=\log_{3} (Cos\frac{\pi }{9})^{2} \cdot \frac{1}{\log_{9} Cos\frac{\pi }{9} } =\\\\\\=\frac{2\log_{3} Cos\frac{\pi }{9} }{\log_{3} (Cos\frac{\pi }{9} )^{\frac{1}{2} } } =\frac{2\log_{3} Cos\frac{\pi }{9} }{\frac{1}{2} \log_{3} Cos\frac{\pi }{9} } } =2:\frac{1}{2} =4$