If sin x + cos x =
1/2
, then what is the value of sin-3- x + cos-3-x?
(Suggestion: Do not nd the individual values of sin x and cos x.)  Choose one: A) 1 /2 B) 3/ 4 C) 9 /16 D) 5/ 8 E) 11/ 16
Since sin x + cos x = 1=2, we get   1   4   = (sin x + cos x)2 = sin2 x + 2 sin x cos x + cos2 x = 1 + 2= 
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
􀀀3=8. Thus,   sin3 x + cos3 x = (sin x + cos x)(sin2 x 􀀀 sin x cos x + cos2 x) =   1/21 +   3/8 =   11/16   correct answer 11/ 16
<result>E</result>
If sin x + cos x =
1/2
, then what is the value of sin-3- x + cos-3-x?
(Suggestion: Do not nd the individual values of sin x and cos x.)