Question

(24-6sin3x-3sin^23x)/6-3sin3x

Answer 1

$\frac{24-6sin3x-3 *sin^{2}3x }{6-3sin3x} =$
1. -3sin²3x-6sin3x+24 квадратный трехчлен, разложить на множители: 
sin3x=t, -3t²-6t+24=0
D=324, t₁=-4, t₂=2
-3sin²3x-6sin3x+24=-3*(sin3x+4)*(sin3x-2)
2. сократить дробь:

$= \frac{-3*(sin3x+4)*(sin3x-2)}{-3*(sin3x-2)} =sin3x+4$

ответ: sin3x+4

Answer 2

To simplify the expression (24 - 6sin(3x) - 3sin^2(3x)) / (6 - 3sin(3x)), let's break it down step by step:

1. Notice that the numerator (24 - 6sin(3x) - 3sin^2(3x)) can be factored: 24 - 6sin(3x) - 3sin^2(3x) = 3(8 - 2sin(3x) - sin^2(3x))

2. Now, let's focus on the denominator (6 - 3sin(3x)): The denominator can be factored out as well: 6 - 3sin(3x) = 3(2 - sin(3x))

3. Substitute the factored forms back into the original expression: (3(8 - 2sin(3x) - sin^2(3x))) / (3(2 - sin(3x)))

4. Cancel out the common factors of 3 in the numerator and denominator: (8 - 2sin(3x) - sin^2(3x)) / (2 - sin(3x))

And there you have it! The simplified form of the expression is (8 - 2sin(3x) - sin^2(3x)) / (2 - sin(3x)).