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 $tg alpha = -4$:

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