Question

1-2sin2acos2a-sin6a-cos6aplease ​

Answer 1

Ответ:

$2 \sin(3a) {}^{2} - \sin(4a) - \sin(6a)$

это ответ

Answer 2

The given expression is 1 - 2sin^2(2a)cos^2(a) - sin^6(a) - cos^6(a).

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

1. Recall the trigonometric identity: sin^2(x) + cos^2(x) = 1.

Using this identity, we can replace sin^6(a) with (sin^2(a))^3 and cos^6(a) with (cos^2(a))^3:

1 - 2sin^2(2a)cos^2(a) - (sin^2(a))^3 - (cos^2(a))^3

2. Next, we can use another trigonometric identity: sin(2x) = 2sin(x)cos(x). This allows us to simplify sin^2(2a)cos^2(a) as follows:

sin^2(2a)cos^2(a) = (2sin(a)cos(a))^2cos^2(a) = 4sin^2(a)cos^4(a)

3. Now, let's substitute this simplification back into the original expression:

1 - 2(4sin^2(a)cos^4(a)) - (sin^2(a))^3 - (cos^2(a))^3

4. Simplify further:

1 - 8sin^2(a)cos^4(a) - sin^6(a) - cos^6(a)

5. Finally, we can use the identity sin^2(a) = 1 - cos^2(a) to substitute for sin^2(a) in the expression:

1 - 8(1 - cos^2(a))cos^4(a) - (1 - cos^2(a))^3 - cos^6(a)

Expanding and simplifying the terms will provide the final result.