Trigonometry Identities

**andymac** · June 18th 2008, 01:47 PM

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.

**TKHunny** · June 18th 2008, 02:24 PM

Originally Posted by andymac

1. 2sinxcos^3x - 2sin^3xcox

2sinxcos^3x - 2sin^3xcox

Factor

$2\sin(x)\cos^{3}(x) - 2\sin^{3}(x)\cos(x)\;=\;2\sin(x)\cos(x)[\cos^{2}(x)-\sin^{2}(x)]$

Both those pieces (inside and outide the []) should look very familiar.

2. Develop a forumula for sin3x in terms of sinx

$\sin(a+b) = \sin(a)\cos(b)\;+\;\sin(b)\cos(a)$

That's almost all you need.

**Moo** · June 18th 2008, 02:25 PM

2. Develop a forumula for sin3x in terms of sinx

Thanks in advance.

$\sin 3x=\sin (2x+x)$

$\sin(a+b)=\sin a\cos b+\sin b\cos a$

And then, you will need these formulae :

$\cos 2x=1-2 \sin^2x$
$\sin 2x=2 \cos x \sin x$
$\cos^2x=1-\sin^2x$

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