# Math Help - sin(6x)/sin(2x) = sin(3x) ?

1. ## sin(6x)/sin(2x) = sin(3x) ?

Is

sin(6x)/sin(2x) = sin(3x)

?

If not, then what would be the correct way of expressing this?

Any input would be greatly appreciated!

2. Originally Posted by s3a
Is

sin(6x)/sin(2x) = sin(3x)

?

If not, then what would be the correct way of expressing this?

Any input would be greatly appreciated!
No, that is not right. A counterexample is $x = \frac{\pi}{4}$

$sin(6x) = sin(3 \times 2x) = 3sin(2x)+4sin^3(2x)$

$
\frac{3sin(2x)+4sin^3(2x)}{sin(2x)} = 3+4sin^2(2x)$

3. sin(6x)/sin(2x) = sin(3x)

(2sin 3x cos 3x)/sin 2x = sin 3x,

that red thing (sin 2x) SHOULD be cos 3x, and 2 should be introduced to the RHS, to generate an identity. . . . see below

(2sin 3x cos 3x)/cos 3x = 2 sin 3x