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

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Prepare for the JH Academic Bowl Test with flashcards and multiple choice questions, including hints and explanations. Elevate your confidence ahead of the exam!

Multiple Choice

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

Explanation:
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.

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