If `cot theta =7/8`
Find the Value of `cot^(2) theta `

Options

A. `7/8`
B. `(49)/64`
C. `56/78`
D. `sqrt(7/8)`

Answer

To find the value of \( \cot^2 \theta \) given that \( \cot \theta = \frac{7}{8} \), we can follow these steps:

### Step 1: Write the expression for \( \cot^2 \theta \)
We know that:
\[ \cot^2 \theta = (\cot \theta)^2 \]

### Step 2: Substitute the value of \( \cot \theta \)
Substituting the given value of \( \cot \theta \):
\[ \cot^2 \theta = \left(\frac{7}{8}\right)^2 \]

### Step 3: Calculate the square of \( \frac{7}{8} \)
Now, we can calculate \( \left(\frac{7}{8}\right)^2 \):
\[ \cot^2 \theta = \frac{7^2}{8^2} = \frac{49}{64} \]

### Step 4: Write the final answer
Thus, the value of \( \cot^2 \theta \) is:
\[ \cot^2 \theta = \frac{49}{64} \]