I have an exam tomorow and I ran in to some problems with the following questions:
1. 2sinxcos^3x - 2sin^3xcox
and
2. Develop a forumula for sin3x in terms of sinx
Thanks in advance.
2sinxcos^3x - 2sin^3xcox
Factor
$\displaystyle 2\sin(x)\cos^{3}(x) - 2\sin^{3}(x)\cos(x)\;=\;2\sin(x)\cos(x)[\cos^{2}(x)-\sin^{2}(x)]$
Both those pieces (inside and outide the []) should look very familiar.
$\displaystyle \sin(a+b) = \sin(a)\cos(b)\;+\;\sin(b)\cos(a)$2. Develop a forumula for sin3x in terms of sinx
That's almost all you need.
$\displaystyle \sin 3x=\sin (2x+x)$2. Develop a forumula for sin3x in terms of sinx
Thanks in advance.
$\displaystyle \sin(a+b)=\sin a\cos b+\sin b\cos a$
And then, you will need these formulae :
$\displaystyle \cos 2x=1-2 \sin^2x$
$\displaystyle \sin 2x=2 \cos x \sin x$
$\displaystyle \cos^2x=1-\sin^2x$