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2. Упростите выражение:

[tex]8 \sin3 \alpha \cdot \cos3 \alpha \cdot \cos6 \alpha \cdot \cos12 \alpha = 4 \sin6 \alpha \cdot \cos6 \alpha \cdot \cos12 \alpha = 2 \sin12 \alpha \cdot \cos12 \alpha = \sin24 \alpha [/tex]

3.

[tex] \tan \alpha = \frac{2}{3} ~~~~;~~~~ \tan \beta = \frac{1}{3} [/tex]

[tex] \tan( \alpha - \beta ) = \frac{ \tan \alpha + \tan \beta }{1 - \tan \alpha \cdot \tan \beta } [/tex]

Подставим:

[tex]\Rightarrow \frac{ \frac{2}{3} + \frac{1}{3} }{1 - \frac{2}{3} \cdot \frac{1}{3} } = \frac{1}{1 - \frac{2}{9} } = \frac{1}{ \frac{7}{9} } = 1\cdot \frac{9}{7} = \frac{9}{7} = 1 \frac{2}{7} [/tex]