Functions of multiple angles prove the equation
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Functions of multiple angles prove the equation

[From: ] [author: ] [Date: 12-05-11] [Hit: ]
......
sin B cos^3B - cos B sin^3B = sin 4B/4

How do i prove this equation?
Please EXPLAIN, thanks in advance!

-
sin4B/4= sinB
please check it. it doesn't sound right.


sinB cos³B -cosB sin³B =

sinB cosB cos²B -cosB sinB sin²B =
factor out sinBcosB

sinBcosB ( cos²B - sin²B) =
use Pythagorian ID

sinBcosB ( 1-sin²B-sin²B) =
sinBcosB (1-2sin²B) =
use double ID

(1/2) sin(2B) (cos(2B) =

use double ID again

(1/2)(1/2)( sin 4B)= (1/4) sin(4B)
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