1) Вычеслите: sin 105

2) Упростите: sin (180-a) + cos (90+a)

3) ctg40*tg140

1) sin105 = sin (60+45) = sin60*cos45+cos60*sin45 = √3/2 * √2/2 + 1/2 * √2/2 = √6/4 + √2/4 = (√6+√2) / 4

2) sin (180-a) + cos (90+a) = sina + (- sina) = sina - sina = 0

3) cos 40/sin40 * sin140/cos140 = (cos40*sin140) / (sin40*cos140) = 1/2 [sin (40+140) - sin (40-140) ] / 1/2 [sin (40+140) + sin (40-140) ] = (sin180+sin100) / (sin180-sin100) = sin100 / (-sin100) = - 1