Answer:
cos(2x) is equal to 17/25
Explanation:
To determine the value of cos(2x), we can use the double angle identity for cosine, which states that cos(2x) = cos²(x) - sin²(x).
Given that sin(x) = -2/5 and cos(x) is positive, we can determine the value of cos(x) using the Pythagorean identity: cos²(x) + sin²(x) = 1.
Let's solve for cos(x):
cos²(x) + sin²(x) = 1
cos²(x) + (-2/5)² = 1
cos²(x) + 4/25 = 1
cos²(x) = 1 - 4/25
cos²(x) = 21/25
Since cos(x) is positive, we take the positive square root:
cos(x) = √(21/25)
cos(x) = 21/25
Now, we can calculate cos(2x) using the double angle identity:
cos(2x) = cos²(x) - sin²(x)
cos(2x) = (21/25)² - (-2/5)²
cos(2x) = 441/625 - 4/25
cos(2x) = (441 - 16)/625
cos(2x) = 425/625
cos(2x) = 17/25
Therefore, cos(2x) is equal to 17/25.