Rewrite with only sin(x) and cos(x). sin(3x)

sin 3x = sin (2x + x)

= sin2x cos x + cos 2x sin x   (using the compound angle identity)

= 2sin x cos x.cos x  (1 - 2sin^2x) sinx     (using identities for sin2x and cos2x)

=  2 sin cos^2 x + sin x - 2 sin^3 x

Bill and Matthew's perceptive of war varies.

Explanation:.

Bill is against slavery and says that they had to suffer slavery till their deaths Even though he hates slavery, he doesn't  have  his heart in it and goes to fight for the South. On the other hand, his brother goes to fight for the North.

Bill feels that neither of them will win the war. This shows both the boys were interested in war.

Bill feels that people have not changed from the ancient time and  some people felt that Bill was a traitor.