Two times the sine of x times the cosine of x equals which expression?

Two times the sine of x times the cosine of x equals which expression?

• A. sin 2x
• B. cos 2x
• C. tan x
• D. sin x cos x

Answer: (A)

Using the double-angle identity, sin 2x = 2 sin x cos x. This means the expression 2 sin x cos x is just another way to write sin 2x, so it matches perfectly. The other expressions describe different trig quantities: cos 2x is a different combination of sin and cos (various forms like cos^2 x − sin^2 x or 1 − 2 sin^2 x), tan x is sin x divided by cos x, and sin x cos x is the product without the extra factor of 2, so it does not equal sin 2x in general.

Using the double-angle identity, sin 2x = 2 sin x cos x. This means the expression 2 sin x cos x is just another way to write sin 2x, so it matches perfectly. The other expressions describe different trig quantities: cos 2x is a different combination of sin and cos (various forms like cos^2 x − sin^2 x or 1 − 2 sin^2 x), tan x is sin x divided by cos x, and sin x cos x is the product without the extra factor of 2, so it does not equal sin 2x in general.