The value of `(tan64^(@))/(cot26^(@))` will be :

Options

A. 0
B. 1
C. `-1`
D. `2 tan 64^(@)`.

Answer

To solve the expression \(\frac{\tan 64^\circ}{\cot 26^\circ}\), we can follow these steps:

### Step 1: Rewrite \(\cot 26^\circ\) using the identity
We know that \(\cot \theta = \frac{1}{\tan \theta}\). Therefore, we can rewrite \(\cot 26^\circ\) as:
\[ \cot 26^\circ = \frac{1}{\tan 26^\circ} \]

### Step 2: Substitute \(\cot 26^\circ\) in the expression
Now substitute \(\cot 26^\circ\) in the original expression:
\[ \frac{\tan 64^\circ}{\cot 26^\circ} = \frac{\tan 64^\circ}{\frac{1}{\tan 26^\circ}} = \tan 64^\circ \cdot \tan 26^\circ \]

### Step 3: Use the identity \(\tan(90^\circ - \theta) = \cot \theta\)
We know from trigonometric identities that:
\[ \tan(90^\circ - \theta) = \cot \theta \]
Thus, we can write:
\[ \tan 64^\circ = \tan(90^\circ - 26^\circ) = \cot 26^\circ \]

### Step 4: Substitute \(\tan 64^\circ\) in the expression
Now substitute \(\tan 64^\circ\) back into the expression:
\[ \tan 64^\circ \cdot \tan 26^\circ = \cot 26^\circ \cdot \tan 26^\circ \]

### Step 5: Simplify the expression
Since \(\cot 26^\circ = \frac{1}{\tan 26^\circ}\), we have:
\[ \cot 26^\circ \cdot \tan 26^\circ = 1 \]

### Conclusion
Thus, the value of \(\frac{\tan 64^\circ}{\cot 26^\circ}\) is:
\[ \boxed{1} \]