+91 how does sin 4a equal to each of the following:
a) 2 sin 2a cos 2a
b)4 sin a cos a - 8 sin^3 a cos a
c) 4 sin a cos a cos 2a
d) 4 sin a cos^3 a - 4 sin^3 a cos a
what are the rules that give you those longass equations from just sin 4a ???
+129899 how does sin 4a equal to each of the following:
a) 2 sin 2a cos 2a
This is just based on the identity that sin2a = 2sinacosa.......so ...sin 4a = sin 2(2a) = 2sin2acos2a
b)4 sin a cos a - 8 sin^3 a cos a
Factor out 4 sina cosa
4 sina cosa [ 1 - 2sin^2A] =
2 [2sin a cos a] [ cos 2a ] =
2 [sin2a] [cos 2a] =
sin 4a
c) 4 sin a cos a cos 2a
2 [2 sina cos a] cos2a =
2 [sin 2a] [ cos 2a] =
sin 4a
d) 4 sin a cos^3 a - 4 sin^3 a cos a
Factor out 4sinacosa =
4 sina cosa [ cos^2 a - sin^2 a] =
4sina cos a [ cos2a] =
2 [2sina cos a ] [cos 2a] =
2 [sin2a] [cos 2a] =
sin 4a
Metallica......looks like we can delay your execution for at least a couple of days.......or so......LOL!!!
+129899 how does sin 4a equal to each of the following:
a) 2 sin 2a cos 2a
This is just based on the identity that sin2a = 2sinacosa.......so ...sin 4a = sin 2(2a) = 2sin2acos2a
b)4 sin a cos a - 8 sin^3 a cos a
Factor out 4 sina cosa
4 sina cosa [ 1 - 2sin^2A] =
2 [2sin a cos a] [ cos 2a ] =
2 [sin2a] [cos 2a] =
sin 4a
c) 4 sin a cos a cos 2a
2 [2 sina cos a] cos2a =
2 [sin 2a] [ cos 2a] =
sin 4a
d) 4 sin a cos^3 a - 4 sin^3 a cos a
Factor out 4sinacosa =
4 sina cosa [ cos^2 a - sin^2 a] =
4sina cos a [ cos2a] =
2 [2sina cos a ] [cos 2a] =
2 [sin2a] [cos 2a] =
sin 4a
Metallica......looks like we can delay your execution for at least a couple of days.......or so......LOL!!!
