**Proof:**

To prove the given equation, we will use the trigonometric identity:

*sin(A) × sin(B) = (1/2) [cos(A - B) - cos(A + B)]*

Let's start by rewriting the given equation using this identity:

*sin(10°) × sin(30°) × sin(50°) × sin(70°) = (1/2) [cos(30° - 10°) - cos(30° + 10°)] × (1/2) [cos(70° - 50°) - cos(70° + 50°)]*

Now, let's simplify the equation step by step:

**Step 1: Simplifying the first bracket**

cos(30° - 10°) - cos(30° + 10°) = cos(20°) - cos(40°)

Using the trigonometric identity:

cos(A - B) - cos(A + B) = -2 sin(A) sin(B)

cos(20°) - cos(40°) = -2 sin(20°) sin(40°)

**Step 2: Simplifying the second bracket**

cos(70° - 50°) - cos(70° + 50°) = cos(20°) - cos(120°)

Using the trigonometric identity:

cos(A - B) - cos(A + B) = -2 sin(A) sin(B)

cos(20°) - cos(120°) = -2 sin(20°) sin(120°)

**Step 3: Combining the simplified brackets**

(-2 sin(20°) sin(40°)) × (-2 sin(20°) sin(120°))

= 4 sin(20°) sin(40°) sin(120°)

**Step 4: Using the trigonometric identity**

sin(120°) = sqrt(3)/2

Therefore, the equation becomes:

4 sin(20°) sin(40°) (sqrt(3)/2)

**Step 5: Simplifying further**

sin(20°) = sin(180° - 20°) = sin(160°)

Using the trigonometric identity:

sin(A) = sin(180° - A)

sin(160°) = sin(20°)

Therefore, the equation becomes:

4 sin(20°) sin(40°) (sqrt(3)/2)

= 4 sin(40°) sin(20°) (sqrt(3)/2)

**Step 6: Applying the trigonometric identity again**

sin(40°) = sin(180° - 40°) = sin(140°)

Using the trigonometric identity:

sin(A) = sin(180° - A)

sin(140°) = sin(40°)

Therefore, the equation becomes:

4 sin(40°) sin(20°) (sqrt(3)/2)

= 4 sin(20°) sin(40°) (sqrt(3)/2)

**Step 7: Final Simplification**

We can see that the equation has the same terms as its original form:

4 sin(20°) sin(40°) (sqrt(3)/2)

Therefore, the final equation is:

sin(10°) × sin(30

Use firmula 2 sin A sin B and 2 CosA sin B