Question

I can't seem to figure this example out.....It's all worked out I just don't see how the identity works to reduce both of these in this way???
cos 3(theta) = cos^3(theta)-3cos(theta)sin^2(theta) and
sin 3(theta) = 3 cos^2(theta)sin(theta)-sin^3(theta)
USING cos^2(theta)+sin^2(theta)=1 identity
then these both go to>>
cos 3(theta)=4cos^3(theta)-3cos(theta)
and sin3(theta)=3sin(theta)-4sin^3(theta)

Answer 1

Here's the equation:

Answer 2

\(\Large \cos^3(\theta)-3\cos(\theta)\sin^2(\theta)\)


\(\Large \cos^2(\theta)+\sin^2(\theta)=1\implies \sin^2(\theta)=1-\cos^2(\theta)\)

so,
\(\Large \cos^3(\theta)-3\cos(\theta)[1-\cos^2(\theta)] \)

do you get this ?

Answer 3

Ok - yes, I see that.

Answer 4

Thank you @hartnn :)

Answer 5

welcome ^_^

Answer 6

ask if anymore doubts ?