1983 AMC 12 Problem 11

Attempt Problem 11 of the 1983 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1983 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

11.

Simplify

\sin(x-y)\cos y

{}+\cos(x-y)\sin y.

1

\sin x

\cos x

\sin x\cos2y

\cos x\cos2y

Recognize the sine addition identity

Apply the sine addition formula with

u=x-y

and

v=y

Taking

u=x-y

and

v=y,

the sine addition identity gives

\begin{aligned} &\sin(x-y)\cos y\\ &\quad+\cos(x-y)\sin y\\ &=\sin((x-y)+y)=\sin x. \end{aligned}

Therefore, the correct answer is B.

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