Question

Сократите: sin(80°+х)/2sin(20°+x/4)sin(70°-x/4)

Answer 1

Решение во вложении-----------------
фигурные скобки писать не надо

Answer 2

To simplify the expression, we'll use trigonometric identities to simplify each term step-by-step.

1. Start with the numerator: sin(80°+x) Using the sum-to-product identity, we have: sin(80°+x) = sin(80°)cos(x) + cos(80°)sin(x)

2. Simplify the denominator: 2sin(20°+x/4)sin(70°-x/4) Using the product-to-sum identities, we have: 2sin(20°+x/4)sin(70°-x/4) = cos(20° - x/4 - 70° + x/4) - cos(20° + x/4 + 70° - x/4)

Simplifying the angles: 2sin(20°+x/4)sin(70°-x/4) = cos(-50°) - cos(90°) Since cos(90°) = 0, we have: 2sin(20°+x/4)sin(70°-x/4) = -cos(50°)

Now, our expression becomes: (sin(80°)cos(x) + cos(80°)sin(x)) / (-cos(50°))

Using the identity sin(90° - θ) = cos(θ), we have: cos(80°) = sin(90° - 80°) = sin(10°)

Finally, the simplified expression is: (sin(80°)cos(x) + sin(10°)sin(x)) / (-cos(50°))