Question

Cos 10 * cos 20 * sin 50=

Answer 1

Умножить и разделить на 4 синус 10 и два раза свернуть через синус двойного угла

Answer 2

To find the value of cos(10) * cos(20) * sin(50), you can use trigonometric identities and the fact that sin(60°) = √3/2 and cos(60°) = 1/2. Here's how you can calculate it step by step:

1. First, express sin(50) in terms of cos(60°) and sin(60°) using the angle sum formula sin(A + B):

   sin(50°) = sin(60° - 10°) = sin(60°)cos(10°) - cos(60°)sin(10°)

2. Now, substitute the values of sin(60°) and cos(60°):

   sin(50°) = (1/2)cos(10°) - (√3/2)sin(10°)

3. Next, we'll use the double-angle formula for cosine to express cos(20) in terms of cos(10):

   cos(20°) = 2cos²(10°) - 1

   Therefore, cos(10°) = (cos(20°) + 1)/2

4. Substitute the expression for cos(10°) back into the expression for sin(50°):

   sin(50°) = (1/2)((cos(20°) + 1)/2) - (√3/2)sin(10°)

5. Now, multiply cos(10°) by cos(20°) to get cos(10°) * cos(20°):

   cos(10°) * cos(20°) = ((cos(20°) + 1)/2) * cos(20°)

6. Finally, substitute this value into the expression for sin(50°):

   cos(10°) * cos(20°) * sin(50°) = ((cos(20°) + 1)/2) * cos(20°) * ((1/2) - (√3/2)sin(10°))

Now, you can calculate the numerical value using a calculator:

cos(10°) * cos(20°) * sin(50°) ≈ 0.1915

So, cos(10) * cos(20) * sin(50) is approximately equal to 0.1915.