Question

If cos theta= 4/5 then find the value of cos2theta

Answer 1

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Answer 2

Given:

The value of cos(theta) is 4/5.

To Find:

The value of cos(2theta) will be?

Solution:

The given problem can be solved using trigonometric identities.

1. The value of cos(theta) is 4/5.

2. The value of sin(theta) can be found from the indentity,

=> sin²(theta) + cos²(theta) = 1,

=> sin²(theta) + (4/5)² = 1,

=>  sin²(theta)  = 1 - (16/25),

=>  sin²(theta) = (25-16)/25,

=>  sin²(theta)  = 9/25,

=> sin(theta) = 3/5.

3. The value of cos(2theta) can be found using the formula,

=> cos(2theta) = cos²(theta) - sin²(theta),

=> cos(2theta) = (4/5)² - (3/5)²,

=> cos(2theta) = (16-9)/25,

=> cos(2theta) = 7/25.

Therefore, the value of cos(2theta) is 7/25.