The value of `(sin65^(@))/(cos25^(@))` is

Options

A. 0
B. 1
C. 2
D. Not defined

Answer

To solve the problem of finding the value of \(\frac{\sin 65^\circ}{\cos 25^\circ}\), we can follow these steps:

### Step 1: Rewrite \(\sin 65^\circ\)
We can use the complementary angle identity in trigonometry, which states that \(\sin(90^\circ - \theta) = \cos(\theta)\).

So, we can rewrite:
\[ \sin 65^\circ = \sin(90^\circ - 25^\circ) \]

### Step 2: Apply the Identity
Using the identity from Step 1:
\[ \sin 65^\circ = \cos 25^\circ \]

### Step 3: Substitute in the Original Expression
Now, substitute \(\sin 65^\circ\) in the original expression:
\[ \frac{\sin 65^\circ}{\cos 25^\circ} = \frac{\cos 25^\circ}{\cos 25^\circ} \]

### Step 4: Simplify the Expression
Now, simplify the fraction:
\[ \frac{\cos 25^\circ}{\cos 25^\circ} = 1 \]

### Final Answer
Thus, the value of \(\frac{\sin 65^\circ}{\cos 25^\circ}\) is:
\[ \boxed{1} \]

---