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Determine cos(2x)
sin(x) = -2÷5 and cos(x) is positive

User Jatin Rana
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1 Answer

5 votes

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.

User Duggu
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