Question

помогите пожалуйста!!!!!!

Answer 1

Ответ:

1.

$\cos( \beta ) + \sin( \beta ) - \sqrt{2} \sin(45 + \beta ) = \\ = \cos( \beta ) + \sin( \beta ) - \sqrt{2} ( \sin(45) \cos( \beta ) + \sin( \beta ) \cos(45)) = \\ = \cos( \beta ) + \sin( \beta ) - \sqrt{2} ( \frac{ \sqrt{2} }{2} \cos( \beta ) + \frac{ \sqrt{2} }{2} \sin( \beta ) ) = \\ = \cos( \beta ) + \sin( \beta ) - \cos( \beta ) - \sin( \beta ) = 0$

2.

$\cos( \beta ) + \sqrt{3} \sin( \beta ) - 2 \cos(60 - \beta ) = \\ = \cos( \beta ) + \sqrt{3} \sin( \beta ) - 2( \cos(60) \cos( \beta ) + \sin(60) \sin( \beta 7) = \\ = \cos( \beta ) + \sqrt{3} \sin( \beta ) - 2( \frac{1}{2} \cos( \beta ) + \frac{ \sqrt{3} }{2} \sin( \beta )) = \\ = \cos( \beta ) + \sqrt{3} \sin( \beta ) - \cos( \beta ) - \sqrt{3} \sin( \beta ) = 0$

3.

$\cos( \beta ) -\sin( \beta ) - \sqrt{2} \sin( 45 - \beta ) = \\ = \cos( \beta ) - \sin( \beta ) - \sqrt{2} ( \sin(45) \cos( \beta ) - \sin( \beta ) \cos(45)) = \\ = \cos( \beta ) - \sin( \beta ) - \sqrt{2} ( \frac{ \sqrt{2} }{2} \cos( \beta ) - \frac{ \sqrt{2} }{2} \sin( \beta )) = \\ = \cos( \beta ) - \sin( \beta ) - \cos( \beta ) + \sin( \beta ) = 0$

4.

$\sqrt{3} \cos( \beta ) + \sin( \beta ) - 2 \cos( 30 - \beta ) = \\ = \sqrt{3} \cos( \beta ) + \sin( \alpha ) - 2( \cos(30) \cos( \beta ) + \sin(30) \sin( \beta )) = \\ = \sqrt{3} \cos( \beta ) + \sin( \beta ) - 2( \frac{ \sqrt{3} }{2} \cos( \beta ) + \frac{1}{2} \sin( \beta ) ) = \\ = \sqrt{3} \cos( \beta ) + \sin( \beta ) - \sqrt{3} \cos( \beta ) - \sin( \beta ) = 0$

24.16

1.

$\frac{ \sin( \alpha + \beta ) - \sin( \alpha - \beta ) }{ \sin( \alpha + \beta ) + \sin( \alpha - \beta ) } = \\ = \frac{ \sin( \alpha ) \cos( \beta ) + \sin( \beta ) \cos( \alpha ) - \sin( \alpha ) \cos( \beta ) + \cos( \alpha ) \sin( \beta ) }{ \sin( \alpha ) \cos( \beta ) + \sin( \beta ) \cos( \alpha ) + \sin( \alpha ) \cos( \beta ) - \cos( \alpha ) \sin( \beta ) } = \\ = \frac{2 \sin( \beta ) \cos( \alpha ) }{2 \sin( \alpha ) \cos( \beta ) } = tg \alpha \times ctg \alpha$

2.

$\frac{ \cos( \alpha + \beta ) + \cos( \alpha - \beta ) }{ \cos( \alpha + \beta ) - \cos( \alpha - \beta ) } = \\ = \frac{ \cos( \alpha ) \cos( \beta ) - \sin( \alpha ) \sin( \beta ) + \cos( \alpha ) \cos( \beta ) + \sin( \alpha ) \sin( \beta ) }{ \cos( \alpha ) \cos( \beta ) - \sin( \alpha ) \sin( \beta ) - \cos( \alpha ) \cos( \beta ) - \sin( \alpha ) \sin( \beta ) } = \\ = \frac{2 \cos( \alpha ) \cos( \beta ) }{ - 2\sin( \alpha ) \sin( \beta ) } = - ctg \alpha \times ctg \beta$

3.

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

4.

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