The value of `cos (2Cos^-1 0.8)` is

Options

A. 0.48
B. 0.96
C. 0.6
D. 0.28

Answer

To find the value of \( \cos(2 \cos^{-1}(0.8)) \), we will follow these steps:

### Step 1: Define the angle
Let \( \theta = \cos^{-1}(0.8) \). This means that \( \cos(\theta) = 0.8 \).

### Step 2: Use the double angle formula
We need to find \( \cos(2\theta) \). We can use the double angle formula for cosine:
\[ \cos(2\theta) = 2\cos^2(\theta) - 1 \]

### Step 3: Calculate \( \cos^2(\theta) \)
Since \( \cos(\theta) = 0.8 \), we can calculate \( \cos^2(\theta) \):
\[ \cos^2(\theta) = (0.8)^2 = 0.64 \]

### Step 4: Substitute into the double angle formula
Now substitute \( \cos^2(\theta) \) into the double angle formula:
\[ \cos(2\theta) = 2(0.64) - 1 \]

### Step 5: Perform the multiplication
Calculate \( 2 \times 0.64 \):
\[ 2 \times 0.64 = 1.28 \]

### Step 6: Subtract 1
Now, subtract 1 from 1.28:
\[ 1.28 - 1 = 0.28 \]

### Conclusion
Thus, the value of \( \cos(2 \cos^{-1}(0.8)) \) is \( 0.28 \).

### Final Answer
\[ \cos(2 \cos^{-1}(0.8)) = 0.28 \]

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