Question

Решите пожалуйста первый и четвертый номера с фотографии.

Answer 1

1. $\frac{cos 2^{\circ}(1+tg^21^{\circ})}{2(1-tg^21^{\circ})}=\frac{(2cos^21^{\circ}-1)(1+tg^21^{\circ})}{2(1-tg^21^{\circ})}=\frac{2cos^21^{\circ} +2sin^21^{\circ}-1 - tg^21^{\circ}}{2(1-tg^21^{\circ})}=\frac{1-tg^21^{\circ}}{2(1-tg^21^{\circ})}=0,5$

4. $\frac{3+2sin \alpha cos \alpha}{sin^2 \alpha + 4 cos^2 \alpha} = \frac{3+2tg \alpha cos^2 \alpha}{tg^2 \alpha cos^2 \alpha + 4 cos^2 \alpha}$

Подставим $tg \alpha = -4$:

$\frac{3-8cos^2 \alpha}{16cos^2 \alpha + 4 cos^2 \alpha}=\frac{3}{20 cos^2 \alpha}-0,4=0,15 \cdot \frac{1}{cos^2 \alpha}-0,4=0,15 \cdot (1+tg^2 \alpha) -0,4 = 0,15 \cdot 17 - 0,4 = 2,15$