Question

Cos∧4а + cos²а · sin²а - cos²а + 1 =

Answer 1

Ответ:

cos(4a)² + cos(a)²sin(a²) + sin(a)²

Answer 2

To simplify the expression, let's break it down step by step:

1. Rewrite cos^4(a) as (cos^2(a))^2.
2. Apply the identity cos^2(a) = 1 - sin^2(a) to obtain (1 - sin^2(a))^2.
3. Expand the square to get (1 - 2sin^2(a) + sin^4(a)).
4. Combine like terms: 1 - 2sin^2(a) + sin^4(a) + cos^2(a)sin^2(a) - cos^2(a) + 1.
5. Rearrange the terms: sin^4(a) - 2sin^2(a) + cos^2(a)sin^2(a) - cos^2(a) + 2.
6. Apply the identity sin^2(a) = 1 - cos^2(a) to obtain sin^4(a) - 2sin^2(a) + (1 - cos^2(a))cos^2(a) - cos^2(a) + 2.
7. Simplify further: sin^4(a) - 2sin^2(a) + cos^2(a) - cos^4(a) - cos^2(a) + 2.
8. Combine like terms: -cos^4(a) - 2sin^2(a) - cos^2(a) + sin^4(a) + 2.
9. Rearrange the terms: sin^4(a) - cos^4(a) - 2sin^2(a) - cos^2(a) + 2.
10. Apply the identity sin^2(a) = 1 - cos^2(a) to obtain (1 - cos^2(a))^2 - cos^4(a) - 2sin^2(a) - cos^2(a) + 2.
11. Expand the square to get 1 - 2cos^2(a) + cos^4(a) - cos^4(a) - 2sin^2(a) - cos^2(a) + 2.
12. Simplify further: 1 - 2cos^2(a) - 2sin^2(a) - cos^2(a) + 2.
13. Combine like terms: 3 - 3cos^2(a) - 2sin^2(a).

Therefore, the simplified expression is 3 - 3cos^2(a) - 2sin^2(a).