Question

Помогите!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

4.

$\cos( 2\alpha ) = 2 \cos {}^{2} ( \alpha ) - 1 = \\ = 2 \times 0.16 - 1 = 0.32 - 1 = - 0.68$

$tg \frac{ \alpha }{2} = \frac{ \sin( \frac{ \alpha }{2} ) }{ \cos( \frac{ \alpha }{2} ) } \\ \\ \sin( \frac{ \alpha }{2} ) = \pm \sqrt{ \frac{1 - \cos( \alpha ) }{2} } = \\ = \sqrt{ \frac{1 + 0.4}{2} } = \sqrt{ \frac{7}{10} } = \frac{ \sqrt{70} }{10} \\ \\ \cos( \frac{ \alpha }{2} ) = \pm \sqrt{ \frac{1 + \cos( \alpha ) }{2} } = \\ = \sqrt{ \frac{1 - 0.4}{2} } = \sqrt{ \frac{3}{10} } = \frac{ \sqrt{30} }{10} \\ \\ tg \frac{ \alpha }{2} = \frac{ \sqrt{70} }{10} \times \frac{10}{ \sqrt{30} } = \sqrt{ \frac{70}{30} } = \\ = \frac{ \sqrt{210} }{30}$

5.

$\frac{ \cos( 2\alpha ) }{ \cos( \alpha ) - \sin( \alpha ) } - 2 \sin( \frac{ \alpha }{2} ) \cos( \frac{ \alpha }{2} ) = \\ = \frac{ \cos {}^{2} ( \alpha ) - \sin {}^{2} ( \alpha ) }{ \cos( \alpha ) - \sin( \alpha ) } - \sin( \alpha ) = \\ = \frac{( \cos( \alpha ) - \sin( \alpha ) )( \cos( \alpha ) + \sin( \alpha ) )}{ \cos( \alpha ) - \sin( \alpha ) } - \sin( \alpha ) = \\ = \cos( \alpha ) + \sin( \alpha ) - \sin( \alpha ) = \cos( \alpha )$