Difference between revisions of "1983 AHSME Problems/Problem 11"

Revision as of 17:46, 26 January 2019

Simplify $\sin (x-y) \cos y + \cos (x-y) \sin y$ .

$\textbf{(A)}\ 1\qquad \textbf{(B)}\ \sin x\qquad \textbf{(C)}\ \cos x\qquad \textbf{(D)}\ \sin x \cos 2y\qquad \textbf{(E)}\ \cos x\cos 2y$

By the addition formula for $\sin$ , this becomes $\sin{((x-y)+y)} = \sin{x}$ , so the answer is $\fbox{B}$ .

Revision as of 12:09, 7 June 2016 (view source) Katzrockso (talk \| contribs) (Created page with "== Problem 11 == Simplify <math>\sin (x-y) \cos y + \cos (x-y) \sin y</math>. <math>\textbf{(A)}\ 1\qquad \textbf{(B)}\ \sin x\qquad \textbf{(C)}\ \cos x\qquad \textbf{(D)}\...")		Revision as of 17:46, 26 January 2019 (view source) Sevenoptimus (talk \| contribs) (Replaced the solution with one that's actually correct) Newer edit →
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	== Solution ==		== Solution ==
−	~~Take~~ <math>~~y=0~~\~~implies~~ \sin(x)</math>, so <math>\fbox{B}</math>	+	By the addition formula for <math>\sin</math>, this becomes <math>\sin{((x-y)+y)} = \sin{x}</math>, so the answer is <math>\fbox{B}</math>.