Question

Известно sina+cosa=1,3. вычислить sina•cosa

Answer 1

Sina умножить на cosa = 2/3

Answer 2

To solve for the product of sin(a) and cos(a), we can use trigonometric identities. One such identity is:

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

Using this identity, we can manipulate the given equation to find sin(a) * cos(a).

Given: sin(a) + cos(a) = 1.3

Let's square both sides of the equation:

(sin(a) + cos(a))^2 = (1.3)^2

Expanding the left-hand side:

sin^2(a) + 2 * sin(a) * cos(a) + cos^2(a) = 1.69

Now, we know that sin^2(a) + cos^2(a) = 1, so we can substitute that in:

1 + 2 * sin(a) * cos(a) = 1.69

Next, rearrange the equation to isolate sin(a) * cos(a):

2 * sin(a) * cos(a) = 1.69 - 1

2 * sin(a) * cos(a) = 0.69

Finally, solve for sin(a) * cos(a):

sin(a) * cos(a) = 0.69 / 2

sin(a) * cos(a) = 0.345

So, the value of sin(a) * cos(a) is approximately 0.345.