Question

Решить ур-ие:
sin6 + cos6*tg42
(6,42-в градусах)

Answer 1

По действиям:
1). $tg 42^{circ} = frac{sin 42^{circ}}{cos 42^{circ}}= frac{sin(45^{circ}-3^{circ})}{cos(45^{circ}-3^{circ})} = frac{sin 45^{circ}*cos 3^{circ}-cos 45^{circ}*sin 3^{circ}}{cos 45^{circ}*cos 3^{circ}+sin 45^{circ}*sin 3^{circ}}=$
$= frac{frac{sqrt{2}}{2}*cos 3^{circ}-frac{sqrt{2}}{2}*sin 3^{circ}}{frac{sqrt{2}}{2}*cos 3^{circ}+frac{sqrt{2}}{2}*sin 3^{circ}}= frac{cos 3^{circ}-sin 3^{circ}}{cos 3^{circ}+sin 3^{circ}}$

2). $cos 6^{circ}* frac{cos 3^{circ}-sin 3^{circ}}{cos 3^{circ}+sin 3^{circ}}= (cos^{2} 3^{circ}- sin ^{2} 3^{circ})* frac{cos 3^{circ}-sin 3^{circ}}{cos 3^{circ}+sin 3^{circ}}=$
$= (cos 3^{circ}- sin 3^{circ})*(cos 3^{circ}+ sin 3^{circ})* frac{cos 3^{circ}-sin 3^{circ}}{cos 3^{circ}+sin 3^{circ}}= (cos 3^{circ}- sin 3^{circ})^{2}=$
$= cos^{2} 3^{circ} -2*cos 3^{circ}*sin 3^{circ} + sin^{2} 3^{circ}= 1-sin 6^{circ}$

3). $sin 6^{circ}+1-sin 6^{circ} = 1$

Ответ: 1.

Answer 2

можно было сделать гораздо-гораздо иррациональней и легче!)