Find the value of `(sin 45^@)/(sin 30^@)`

Options

A. 2
B. `sqrt2`
C. `2sqrt2`
D. `1/sqrt2`

Answer

To find the value of \(\frac{\sin 45^\circ}{\sin 30^\circ}\), we can follow these steps:

### Step 1: Identify the values of \(\sin 45^\circ\) and \(\sin 30^\circ\)
- The value of \(\sin 45^\circ\) is \(\frac{1}{\sqrt{2}}\).
- The value of \(\sin 30^\circ\) is \(\frac{1}{2}\).

### Step 2: Substitute the values into the expression
Now we can substitute these values into the expression:
\[ \frac{\sin 45^\circ}{\sin 30^\circ} = \frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}} \]

### Step 3: Simplify the expression
To simplify the fraction, we can multiply by the reciprocal of the denominator:
\[ \frac{1}{\sqrt{2}} \times \frac{2}{1} = \frac{2}{\sqrt{2}} \]

### Step 4: Rationalize the denominator
To rationalize the denominator, we multiply the numerator and the denominator by \(\sqrt{2}\):
\[ \frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}{2} = \sqrt{2} \]

### Final Answer
Thus, the value of \(\frac{\sin 45^\circ}{\sin 30^\circ}\) is \(\sqrt{2}\).

---