Question

помогите плиз срочно​

Answer 1

Ответ:

1.

а

$1 - \sin {}^{2} ( \beta ) = \cos {}^{2} ( \beta )$

б

$\sin {}^{2} ( \beta ) - 1 = - (1 - \sin {}^{2} ( \beta )) = - \cos {}^{2} ( \beta )$

в

$\cos( \alpha ) tg( \alpha ) = \cos( \alpha ) \times \frac{ \sin( \alpha ) }{ \cos( \alpha ) } = \sin( \alpha )$

г

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

д

$\frac{1}{ \cos {}^{2} ( \beta ) } - 1 = \frac{1 - \cos {}^{2} ( \beta ) }{ \cos {}^{2} ( \beta ) } = \frac{ \sin {}^{2} ( \beta ) }{ \cos {}^{2} ( \beta ) } = {tg}^{2} (\beta )$

2.

а

$2 \sin(30 ^ {\circ}) + 2 \cos(60 ^ {\circ}) = 2 \times \frac{1}{2} + 2 \times \frac{1}{2} = 2$

б

$(4tg \frac{\pi}{4} + ctg \frac{\pi}{4} ) \div 5 = (4 \times 1 + 1) \div 5 = \\ = 5 \div 5 = 1$

в

$7 \sin( \frac{\pi}{4} ) + 3 \cos(45 ^ {\circ}) = 7 \times \frac{ \sqrt{2} }{2} + 3 \times \frac{ \sqrt{2} }{2} = \\ = 10 \times \frac{ \sqrt{2} }{2} = 5 \sqrt{2}$

г

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

д

$ctg \frac{\pi}{2} + tg0 ^ {\circ} + 5 = 0 + 0 + 5 = 5$

3.

$\frac{ \sin(x) + \cos(x) }{1 + tgx} = \frac{ \sin(x) + \cos(x) }{1 + \frac{ \sin(x) }{ \cos(x) } } = \\ = ( \sin(x) + \cos(x)) \times \frac{ \cos(x) }{ \sin(x) + \cos(x) } = \\ = \cos(x)$

4.

$\frac{1}{ \sqrt{1 - \cos {}^{2} (x) } } + \sqrt{1 + {ctg}^{2} x} = \\ = \frac{1}{ \sqrt{ \sin {}^{2} (x) } } + \sqrt{1 + \frac{ \cos {}^{2} (x) }{ \sin {}^{2} (x) } } = \\ = \frac{1}{ | \sin(x) | } + \sqrt{ \frac{ \sin {}^{2} (x) + \cos {}^{2} (x) }{ \sin {}^{2} (x) } } = \\ = \frac{1}{| \sin(x) | } + \sqrt{ \frac{1}{ \sin {}^{2} (x) } } = \frac{1}{ | \sin(x) | } + \frac{1}{ | \sin(x) | } = \\ = \frac{2}{ | \sin(x) | }$