Question

Sin(a-3П/2)cos(2П-a)-sin(П-a)sin(П+a)​

Answer 1

Ответ:

Пошаговое объяснение:

sin(a-3П/2)cos(2П-a)-sin(П-a)sin(П+a) = -(-cos a)* cos a - sin a * (-sin a) = cos²a + sin²a = 1

Answer 2

To simplify the expression sin(a - 3π/2)cos(2π - a) - sin(π - a)sin(π + a), you can use trigonometric identities. Here's how you can do it step by step:

1. Start with the given expression: sin(a - 3π/2)cos(2π - a) - sin(π - a)sin(π + a)

2. Use the following trigonometric identity for cos(2π - a): cos(2π - a) = cos(-a) = cos(a)

3. Now, your expression becomes: sin(a - 3π/2)cos(a) - sin(π - a)sin(π + a)

4. Use the following trigonometric identities for sin(π - a) and sin(π + a): sin(π - a) = sin(a) sin(π + a) = -sin(a)

5. Substitute these values into the expression: sin(a - 3π/2)cos(a) - sin(a)(-sin(a))

6. Distribute sin(a) in the second term: sin(a - 3π/2)cos(a) + sin(a)sin(a)

7. Finally, you can factor out sin(a): sin(a)[cos(a - 3π/2) + sin(a)]

So, the simplified expression is sin(a)[cos(a - 3π/2) + sin(a)].