sin B cos^3B - cos B sin^3B = sin 4B/4
How do i prove this equation?
Please EXPLAIN, thanks in advance!
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)
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)