Question

Evaluate f(x)=4sin(x)cos(x) and choose the correct option from the given choices (A, B, C, D).

(A). sin 2 x \quad
(B)-cos 2 x \quad
(C) 2 sin ^{2} x
(D) -2 \cos ^{2} x

Answer 1

The function f(x)=4sin(x)cos(x) can be simplified using the double angle identity for sine to 2sin(2x), which matches choice (A) sin(2x).

Step-by-step explanation:

To evaluate the function f(x)=4sin(x)cos(x), we can use the trigonometric identity for the double angle of sine, which states that sin(2x) = 2sin(x)cos(x). Therefore, we can simplify the given function by substituting with the double angle of sine:

f(x) = 4 × sin(x)cos(x)

f(x) = 4 × ½ sin(2x)

f(x) = 2sin(2x)

Hence, we have transformed the original expression into a simpler form, which matches one of the given choices. In this case, the correct option is (A) sin(2x).