I am studying for a test and can not firgure out how to do these problems:
Prove the identity:
1) sin 3x = ( sin x ) ( 4 cos^2(x) - 1 )
2) sin 3x = ( sin x ) ( 3 - 4 sin^2 (x) )
3) sin^4 (x) = ( 1/8 ) ( 3 - 4 cos 2x + cos 4x )
Solve the half angle Identities for all the solutions for the interval [ 0 , 2? )
1) cos^2 (x) = sin^2 (x/2) or cos^2 (x) = sin^2 ( (1/2) x)
2) sin^2 (x) = cos^2 (x/2)
................... 1 - cos (x) /
3) tan (x/2) = 1 +cos (x)
4) sin^2 (x/2) = 2 cos^2 (x) - 1
I really hope some one can figure these out cause i really could not!!
Prove the identity:
1) sin 3x = ( sin x ) ( 4 cos^2(x) - 1 )
2) sin 3x = ( sin x ) ( 3 - 4 sin^2 (x) )
3) sin^4 (x) = ( 1/8 ) ( 3 - 4 cos 2x + cos 4x )
Solve the half angle Identities for all the solutions for the interval [ 0 , 2? )
1) cos^2 (x) = sin^2 (x/2) or cos^2 (x) = sin^2 ( (1/2) x)
2) sin^2 (x) = cos^2 (x/2)
................... 1 - cos (x) /
3) tan (x/2) = 1 +cos (x)
4) sin^2 (x/2) = 2 cos^2 (x) - 1
I really hope some one can figure these out cause i really could not!!