Question

Пункт 2, срочно!!!!!!!!!!!!!!!

Answer 1

Ответ:

1)

$\cos^{4}(x) - \sin ^{4} (x) = ( \cos^{2} (x) - \sin^{2}(x) )( \cos^{2}(x) + \sin ^{2} (x) ) = \cos(2x) \times 1 = \cos(2x)$

$f(x) = \cos(2x)$

2)

$\cos( \alpha) = - \frac{2}{ \sqrt{7} } \\ \alpha = \arccos( - \frac{2}{ \sqrt{7} } ) \\ \alpha = \pi - \arccos( \frac{2}{ \sqrt{7} } )$

$f( \alpha ) = \cos(2(\pi - \arccos( \frac{2}{ \sqrt{7} }) )$

$\cos(2\pi - 2 \arccos( \frac{2}{ \sqrt{7} } )) = \cos(2 \arccos( \frac{2}{ \sqrt{7} } )) = \cos ^{2} ( \arccos( \frac{2}{ \sqrt{7} } )) - \sin^{2} ( \arccos( \frac{2}{ \sqrt{7} } ) ) = {( \frac{2}{ \sqrt{7} }) }^{2} - { \sqrt{1 - ( \frac{2}{ \sqrt{7} } )^{2} } }^{2} = \frac{4}{7} - (1 - \frac{4}{7} ) = \frac{4}{7} - \frac{3}{7} = \frac{1}{7}$

$f( \alpha ) = \frac{1}{7}$