Find the value of `sin 1^@ *sin2^@* sin3^@........ Sin 180^@.........sin196^@`.

Answer

To find the value of the expression \( \sin 1^\circ \cdot \sin 2^\circ \cdot \sin 3^\circ \cdots \sin 180^\circ \cdots \sin 196^\circ \), we can follow these steps:

### Step 1: Identify the sine of key angles
We know that \( \sin 180^\circ = 0 \).

### Step 2: Multiply the sine values
Since \( \sin 180^\circ = 0 \), when we multiply \( \sin 1^\circ \cdot \sin 2^\circ \cdot \sin 3^\circ \cdots \sin 180^\circ \cdots \sin 196^\circ \), the product will include \( \sin 180^\circ \).

### Step 3: Conclude the result
Any product that includes a factor of 0 will result in 0. Therefore, the entire product \( \sin 1^\circ \cdot \sin 2^\circ \cdot \sin 3^\circ \cdots \sin 180^\circ \cdots \sin 196^\circ \) equals 0.

### Final Answer:
Thus, the value of \( \sin 1^\circ \cdot \sin 2^\circ \cdot \sin 3^\circ \cdots \sin 180^\circ \cdots \sin 196^\circ = 0 \).

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