Question

Partea 2 Ex 2 dau coroana!!!!!

Answer 1

Răspuns:

Explicație pas cu pas:

a)

cos²(a) + sin²(a) = 1

cos²(a) = 1 - sin²(a)

cos(a) = √[1 - sin²(a)] = √[1- (3/5)²] = √(1 - 9/25) = √(25/25 - 9/25) = √[(25-9)/25] = √(16/25) = 4/5

b)

sin(a+b) = sin(a)*cos(b) + cos(a)*sin(b)

cos²(b) + sin²(b) = 1

cos²(b) = 1 - sin²(b)

cos(b) = √[1 - sin²(b)] = √[1- (5/13)²] = √(1 - 25/169) = √(169/169 - 25/169) = √[(169 -25)/169] = √(144/169) = 12/13

sin(a+b) = sin(a)*cos(b) + cos(a)*sin(b = (3/5)*(12/13)*(4/5)*(5/13) = (3*4*5*12)/(5*5*13*13) = 144/845

c)

Notam sin(x) = y

$[\sqrt{1+ sin(x)} +\sqrt{1 -sin(x)}]^2+[\sqrt{1+ sin(x)} -\sqrt{1 -sin(x)}]^2 =$

$(\sqrt{1+ y} +\sqrt{1 -y})^2+(\sqrt{1+y} -\sqrt{1-y})^2 =$

$=(\sqrt{1+ y})^2 +2*\sqrt{1+y}*\sqrt{1- y} +(\sqrt{1- y})^2+ (\sqrt{1+ y})^2 -2*\sqrt{1+y}*\sqrt{1- y} +(\sqrt{1- y})^2 =$

$=1+ y +2*\sqrt{1+y}*\sqrt{1- y} +1- y+ 1+ y-2*\sqrt{1+y}*\sqrt{1- y} +1- y = 4$