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

Latest revision as of 23:47, 19 February 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 $\boxed{\textbf{(B)}}$ .

1983 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

@@ Line 10: / Line 10: @@
 == 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>\boxed{\textbf{(B)}}</math>.
+==See Also==
+{{AHSME box|year=1983|num-b=10|num-a=12}}
+{{MAA Notice}}