Question

How to simplify -4x cos(x^2)sin(x^2)?

a) -2 sin(2x^2)
b) 2 sin(2x^2)
c) -2 cos(2x^2)
d) 2 cos(2x^2)

Answer 1

The expression -4x cos(x^2)sin(x^2) can be simplified using the double angle identity for sine, resulting in -2 sin(2x^2), which is option (a).

Step-by-step explanation:

The student asked how to simplify -4x cos(x^2)sin(x^2). To simplify this expression, we can use the trigonometric identity for the sine of a double angle, which is sin(2θ) = 2sin(θ)cos(θ). Applying this identity with θ being x^2, we get the following:

-4x cos(x^2)sin(x^2) = -2 · 2sin(x^2)cos(x^2) = -2sin(2x^2)

Therefore, the simplified form of the expression is -2 sin(2x^2), which corresponds to option (a).