SOLUTION: Which expression is equivalent to sin(0.6x)-sin(0.4x)? a. 2cos(0.5x)sin(0.1x) b. 2cos(0.5x)cos(0.1x) c. 2sin(0.5x)sin(0.1x) d.-2sin(0.5x)sin(0.1x) e.-2cos(0.5x)sin(0.1x)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Which expression is equivalent to sin(0.6x)-sin(0.4x)? a. 2cos(0.5x)sin(0.1x) b. 2cos(0.5x)cos(0.1x) c. 2sin(0.5x)sin(0.1x) d.-2sin(0.5x)sin(0.1x) e.-2cos(0.5x)sin(0.1x)       Log On


   

Question 1170381: Which expression is equivalent to sin(0.6x)-sin(0.4x)?
a. 2cos(0.5x)sin(0.1x)
b. 2cos(0.5x)cos(0.1x)
c. 2sin(0.5x)sin(0.1x)
d.-2sin(0.5x)sin(0.1x)
e.-2cos(0.5x)sin(0.1x)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

sin%280.6x%29-sin%280.4x%29
let u=0.1x
then we have
sin%286u%29-sin%284u%29
use the following identity : sin%28s+%29-+sin%28t+%29=2cos%28%28s%2Bt%29%2F2%29sin%28%28s-t%29%2F2%29+where s=6u and+t=4u
sin%286u+%29-+sin%284u+%29=2cos%28%286u%2B4u%29%2F2%29sin%28%286u-4u%29%2F2%29
sin%286u+%29-+sin%284u+%29=2cos%2810u%2F2%29sin%282u%2F2%29
sin%286u+%29-+sin%284u+%29=2cos%285u%29sin%28u%29 ............since u=0.1x
sin%286%2A0.1x+%29-+sin%284%2A0.1x+%29=2cos%285%2A0.1x%29sin%280.1x%29
sin%280.6x+%29-+sin%280.4x+%29=2cos%280.5x%29sin%280.1x%29

so, answer is
a. 2cos%280.5x%29sin%280.1x%29