Question

Найдите значение cos^2 a/2, если sina=-1/√5 и 0

Answer 1

Ответ:

Объяснение:

Если sina = -1/√5 , то

cosa = ±√(1 - sin²a) = ±√(1 - (-1/√5)²) = ±√4/5 = ±2/√5

cos²a/2 = (1 + cosa)/2

cos²a/2 = (1 ± 2/√5))/2

Если  sina = 0, то cosa = 1

cos²a/2 = (1 + 1)/2 = 1

Answer 2

To find the value of cos^2(a/2), we can use the half-angle identity for cosine, which is given by:

cos^2(a/2) = (1 + cos(a)) / 2

Given that sin(a) = -1/√5 and 0 < a < π/2, we can determine the value of cos(a) using the Pythagorean identity:

sin^2(a) + cos^2(a) = 1

Let's first find the value of cos(a):

sin^2(a) + cos^2(a) = 1 (-1/√5)^2 + cos^2(a) = 1 1/5 + cos^2(a) = 1 cos^2(a) = 1 - 1/5 cos^2(a) = 4/5

Now, let's find the value of cos(a/2) using the half-angle formula:

cos^2(a/2) = (1 + cos(a)) / 2 cos^2(a/2) = (1 + 4/5) / 2 cos^2(a/2) = (9/5) / 2 cos^2(a/2) = 9/10

So, the value of cos^2(a/2) is 9/10.