Prove the sin 2x + sin 4x + cos 2x + cos 4x = 2 sqrt.2 cos x sin
(3x + pi/4)
Hence find all the angles x between 0 and pi inclusive for
which
sin 2x + sin 4x + cos 2x + cos 4x = 0
so i used:
2sqrt.2 cos x sin(3x + pi/4) = 0
cos x =
0
sin(3x + pi/4) = 0, pi, 2 pi
x = pi/2, 3 pi/2
(rej) x
= -pi/4,(rej) pi/12, 5pi/12
however the answers are pi/4, pi/2, 7pi/12 and 11pi/12...
I subbed my answers into 2sqrt.2 cos x sin(3x + pi/4)
=0 and it is correct. however, when substituted into sin
2x + sin 4x + cos 2x + cos 4x, i got another answer. but if you use
the book's answer and sub it into sin 2x + sin 4x + cos 2x + cos
4x, you get 0. but then again, isnt sin 2x + sin 4x + cos
2x + cos 4x = 2 sqrt.2 cos x sin (3x + pi/4), as
stated ? if that is the case, there shouldn't be
anything amiss with my answers.
it would be of great help if someone could screen through this.
thanks a million times.