Question

Simplify the expression −12cos ² (x)sin(x)÷3sin(x).

A) −4cos ² (x)
B) −12cos ² (x)
C) −4cos(x)
D) −12cos(x)

Answer 1

To simplify −12cos²(x)sin(x)÷3sin(x), cancel the sin(x) terms and divide by 3 to get −4cos²(x), which is answer choice A).

Step-by-step explanation:

To simplify the expression −12cos²(x)sin(x)÷3sin(x), we first look to cancel out any common factors. In this case, we see that both terms in the numerator and the denominator have a sin(x), so we can cancel these terms out. After canceling out the sin(x), we are left with −12cos²(x)÷3 which simplifies to −4cos²(x). To simplify the expression, divide -12 by 3 to get -4, and the simplified expression is -4cos²(x).

The steps are as follows:

1. Identify common factors in the numerator and denominator: sin(x).
2. Cancel out the common factors: sin(x)/sin(x) = 1.
3. Simplify the remaining expression: −12cos²(x)÷3 = −4×(cos²(x)).

Thus, the simplified expression is −4cos²(x), which corresponds to answer choice A).