Ответ:

[tex] \cos( \alpha ) = \frac{4}{5} [/tex]

[tex] \sin( \alpha ) = \sqrt{1 - \cos^{2} ( \alpha ) } [/tex]

[tex] \sin( \alpha ) = \sqrt{1 - {( \frac{4}{5} )}^{2} } = \sqrt{1 - \frac{16}{25} } = \sqrt{ \frac{9}{25} } = \frac{3}{5} [/tex]

[tex] \tan( \alpha ) = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } [/tex]

[tex] \tan( \alpha ) = \frac{ \frac{3}{5} }{ \frac{4}{5} } = \frac{3}{4} [/tex]

1)

[tex] \sin(2 \alpha ) = 2 \sin( \alpha ) \cos( \alpha ) [/tex]

[tex] \sin(2 \alpha ) = 2 \times \frac{3}{5} \times \frac{4}{5} = \frac{24}{25} [/tex]

2)

[tex] \cos(2 \alpha ) = \cos^{2} ( \alpha ) - \sin^{2} ( \alpha ) [/tex]

[tex] \cos(2 \alpha ) = {( \frac{4}{5} )}^{2} - {( \frac{3}{5}) }^{2} = \frac{16}{25} - \frac{9}{25} = \frac{7}{25} [/tex]

3)

[tex] \tan(2 \alpha ) = \frac{2 \tan( \alpha ) }{1 - \tan^{2} ( \alpha ) } [/tex]

[tex] \tan(2 \alpha ) = \frac{2 \times \frac{3}{4} }{1 - {( \frac{3}{4}) }^{2} } = \frac{ \frac{3}{2} }{1 - \frac{9}{16} } = \frac{ \frac{3}{2} }{ \frac{7}{16} } = \frac{3}{2} \times \frac{16}{7} = \frac{24}{7} [/tex]