Question

10 ctg 3 п/4 × sin 5 п/4 cos 7п/4

Answer 1

666°666°666°666°666°666°

Answer 2

To calculate the given expression, let's first evaluate the trigonometric functions for the given angles:

1. ctg(3π/4) = 1 / tan(3π/4) = 1 / (-1) = -1
2. sin(5π/4) = -√2 / 2
3. cos(7π/4) = cos(π/4) = √2 / 2

Now, let's substitute these values into the expression:

-1 * (-√2 / 2) * (√2 / 2)

Now, simplify the expression step-by-step:

-1 * (-√2 * √2) / (2 * 2)

-1 * (-2) / 4

2 / 4

Finally, simplify the fraction:

2 / 4 = 1 / 2

So, the result of the expression is 1/2.