1)Вычеслите: sin 105 2) Упростите: sin(180-a)+cos (90+a) 3) ctg40*tg140

Question

1)Вычеслите: sin 105

2) Упростите: sin(180-a)+cos (90+a)

3) ctg40*tg140

Answer 1

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