Question

Sin(40° + x)sin(x – 50°) = 1.​

Answer 1

Вот, решение этого примера

Answer 2

To solve the equation sin(40° + x)sin(x - 50°) = 1, we can use trigonometric identities and properties.

First, let's rewrite the equation:

sin(40° + x)sin(x - 50°) = 1

Now, we'll use the product-to-sum identity for sine, which states that sin(A)sin(B) = 0.5[cos(A - B) - cos(A + B)]:

0.5[cos((40° + x) - (x - 50°)) - cos((40° + x) + (x - 50°))] = 1

Now, simplify the equation further:

0.5[cos(90°) - cos(90° + 2x - 50°)] = 1

Since cos(90°) = 0 and cos(90° + 2x - 50°) = cos(40° + 2x), the equation becomes:

0.5[0 - cos(40° + 2x)] = 1

Now, we have:

-0.5cos(40° + 2x) = 1

To isolate cos(40° + 2x), divide both sides by -0.5:

cos(40° + 2x) = -2

Now, we need to find the angle whose cosine is -2. However, there is no real angle whose cosine is -2. Therefore, the equation sin(40° + x)sin(x - 50°) = 1 has no real solutions.